{"id":4552,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/"},"modified":"2018-05-07T10:14:36","modified_gmt":"2018-05-07T04:44:36","slug":"ncert-solutions-class-12-maths-exercise-4-5","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 4.5"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Determinants\" >NCERT Solutions class 12 Maths Determinants<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#Find_the_inverse_of_the_matrix_if_it_exists_given_in_Exercise_5_to_11\" >Find the inverse of the matrix (if it exists) given in Exercise 5 to 11.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-2\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#12_Let_A_and_B_verify_that\" >12. Let A = \u00a0and B = \u00a0verify that \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-3\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#13_If_A_show_that_A2_%E2%80%93_5A_7I_0_Hence_find\" >13. If A = , show that A2 \u2013 5A + 7I = 0. Hence find \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-4\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#14_For_the_matrix_A_find_numbers_and_such_that\" >14. For the matrix A = \u00a0find numbers \u00a0and \u00a0such that \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-5\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#15_For_the_matrix_A_show_that_Hence_find\" >15. For the matrix A = , show that \u00a0Hence find<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-6\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#16_If_A_verify_that_and_hence_find\" >16. If A = , verify that \u00a0and hence find<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-7\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#17_Let_A_be_a_non-singular_matrix_of_order_3_x_3_Then_is_equal_to\" >17. Let A be a non-singular matrix of order 3 x 3. Then \u00a0is equal to:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-8\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#18_If_A_is_an_invertible_matrix_of_order_2_then_det_is_equal_to\" >18. If A is an invertible matrix of order 2, then det \u00a0is equal to:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#NCERT_Solutions_class_12_Maths_Exercise_45-9\" >NCERT Solutions class 12 Maths Exercise 4.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/#CBSE_App_for_Class_12\" >CBSE App for Class 12<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 4.5 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-determinants\/1288\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Determinants \u00a0<\/a>as PDF<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20pic.jpg\" alt=\"NCERT Solutions class 12 Maths Exercise 4.5\" width=\"175\" height=\"228\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Determinants\"><\/span>NCERT Solutions class 12 Maths Determinants<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><strong>Find adjoint of each of the matrices in Exercise 1 and 2.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>1. <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image001.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Here A = <img decoding=\"async\" style=\"height: 51px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image002.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0A<sub>11<\/sub> = Cofactor of <img decoding=\"async\" style=\"height: 30px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">A<sub>12<\/sub> = Cofactor of <img decoding=\"async\" style=\"height: 30px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\">A<sub>21<\/sub> = Cofactor of <img decoding=\"async\" style=\"height: 30px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\">A<sub>22<\/sub> = Cofactor of <img decoding=\"async\" style=\"height: 30px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 51px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image011.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>2. <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image012.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Here A = <img decoding=\"async\" style=\"height: 75px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 110px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image015.png\" \/>\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image016.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image018.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 158px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image020.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image022.png\" \/> <img decoding=\"async\" style=\"height: 49px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 177px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 75px; width: 376px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image025.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>Verify A (adj. A) = <\/strong><img decoding=\"async\" style=\"height: 26px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image026.png\" \/><strong>\u00a0in Exercise 3 and 4.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>3. <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image027.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/> adj. A = <img decoding=\"async\" style=\"height: 49px; width: 82px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0A.(adj. A) = <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image028.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 82px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image030.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image031.png\" \/>\u00a0\u00a0\u2026..(i)<\/p>\n<p style=\"text-align: justify;\">Again\u00a0 (adj. A). A = <img decoding=\"async\" style=\"height: 49px; width: 82px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image029.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image032.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image031.png\" \/>\u00a0\u00a0\u00a0 \u2026..(ii)<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 49px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image033.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 189px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\">Again\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 226px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image035.png\" \/>\u00a0\u00a0\u00a0 \u2026..(iii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0From eq. (i), (ii) and (iii)\u00a0 A. (adj. A) = (adj. A). A = <img decoding=\"async\" style=\"height: 26px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image026.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>4. <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image036.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 75px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0\u00a0 <img decoding=\"async\" style=\"height: 75px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image039.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image040.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image041.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image042.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 182px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image043.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image044.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image045.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image046.png\" \/>\u00a0\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 176px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image048.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 75px; width: 359px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0A. (adj. A) = <img decoding=\"async\" style=\"height: 75px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image037.png\" \/><img decoding=\"async\" style=\"height: 75px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 222px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image052.png\" \/> \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">Again\u00a0 (adj. A). A = <img decoding=\"async\" style=\"height: 75px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image050.png\" \/><img decoding=\"async\" style=\"height: 75px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 269px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image052.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\">And <img decoding=\"async\" style=\"height: 75px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 26px; width: 308px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">Also <img decoding=\"async\" style=\"height: 75px; width: 173px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image055.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image052.png\" \/>\u00a0\u00a0\u00a0 \u2026\u2026\u2026.(iii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0From eq. (i), (ii) and (iii)\u00a0 A. (adj. A) = (adj. A). A = <img decoding=\"async\" style=\"height: 26px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image026.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Find_the_inverse_of_the_matrix_if_it_exists_given_in_Exercise_5_to_11\"><\/span><strong>Find the inverse of the matrix (if it exists) given in Exercise 5 to 11.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>5. <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image056.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 49px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image058.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image059.png\" \/>\u00a00<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0Matrix A is non-singular and hence <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>\u00a0exist.<\/p>\n<p style=\"text-align: justify;\">Now adj. A = <img decoding=\"async\" style=\"height: 49px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image061.png\" \/>\u00a0And <img decoding=\"async\" style=\"height: 50px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image062.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>6. <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image063.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 49px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image063.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image064.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0Matrix A is non-singular and hence <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>\u00a0exist.<\/p>\n<p style=\"text-align: justify;\">Now adj. A = <img decoding=\"async\" style=\"height: 49px; width: 70px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image066.png\" \/>\u00a0And <img decoding=\"async\" style=\"height: 50px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image067.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>7. <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image068.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 75px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image069.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image070.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 232px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image071.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>\u00a0exists.<\/p>\n<p style=\"text-align: justify;\">A<sub>11<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image072.png\" \/>,\u00a0 A<sub>12<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image073.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>13<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image074.png\" \/>,\u00a0\u00a0 A<sub>21<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image075.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>22<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image076.png\" \/>,\u00a0\u00a0 A<sub>23<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image077.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>31<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image078.png\" \/>,\u00a0\u00a0 A<sub>32<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image079.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>33<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 142px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image080.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 75px; width: 233px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image081.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 253px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image082.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>8. <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image083.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 75px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image084.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 75px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image085.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image086.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>\u00a0exists.<\/p>\n<p style=\"text-align: justify;\">A<sub>11<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image087.png\" \/>, A<sub>12<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image088.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>13<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image089.png\" \/>, A<sub>21<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image090.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>22<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image091.png\" \/>, A<sub>23<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image092.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>31<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image093.png\" \/>,\u00a0\u00a0 A<sub>32<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image094.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>33<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image095.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 75px; width: 226px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 252px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image097.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>9. <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image098.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 75px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image099.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image100.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image101.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>\u00a0exists.<\/p>\n<p style=\"text-align: justify;\">A<sub>11<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 170px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image102.png\" \/>, A<sub>12<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image103.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>13<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 154px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image104.png\" \/>, A<sub>21<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image105.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>22<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image106.png\" \/>, A<sub>23<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image107.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>31<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 150px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image108.png\" \/>,\u00a0 A<sub>32<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 154px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image109.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>33<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image110.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 75px; width: 246px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image111.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 272px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image112.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>10. <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image113.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 75px; width: 110px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image114.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 75px; width: 130px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image115.png\" \/>= <img decoding=\"async\" style=\"height: 26px; width: 262px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image116.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>\u00a0exists.<\/p>\n<p style=\"text-align: justify;\">A<sub>11<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image117.png\" \/>,\u00a0 A<sub>12<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image118.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>13<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image119.png\" \/>, A<sub>21<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 164px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image120.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>22<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image121.png\" \/>, A<sub>23<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image122.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>31<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image123.png\" \/>, A<sub>32<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image124.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>33<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image125.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 75px; width: 238px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image126.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 381px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image127.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>11. <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image128.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let A = <img decoding=\"async\" style=\"height: 75px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image129.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 162px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image130.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 30px; width: 360px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image131.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>\u00a0exists.<\/p>\n<p style=\"text-align: justify;\">A<sub>11<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 261px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image132.png\" \/>,<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 30px; width: 166px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image133.png\" \/><\/p>\n<p style=\"text-align: justify;\">A<sub>12<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image134.png\" \/>, A<sub>13<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 174px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image135.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>21<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 201px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image136.png\" \/>,\u00a0\u00a0 A<sub>22<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 253px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image137.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>23<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 212px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image138.png\" \/>,\u00a0 A<sub>31<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image139.png\" \/>,<\/p>\n<p style=\"text-align: justify;\">A<sub>32<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 222px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image140.png\" \/>, A<sub>33<\/sub> = <img decoding=\"async\" style=\"height: 49px; width: 218px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image141.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0adj. A = <img decoding=\"async\" style=\"height: 75px; width: 329px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image142.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 448px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image143.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-2\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_Let_A_and_B_verify_that\"><\/span><strong>12. Let A = <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image144.png\" \/><\/strong><strong>\u00a0and B = <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image145.png\" \/><\/strong><strong>\u00a0verify that <\/strong><strong><img decoding=\"async\" style=\"height: 30px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image146.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: Matrix A = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image144.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image147.png\" \/>\u00a0= 15 \u2013 14 = 1 <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image148.png\" \/>\u00a00<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 50px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image149.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image150.png\" \/><\/p>\n<p style=\"text-align: justify;\">Matrix B = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image151.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 70px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image152.png\" \/>\u00a0= 54 \u2013 56 = <img decoding=\"async\" style=\"height: 17px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image153.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image148.png\" \/>\u00a00<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 50px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image154.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now AB = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image144.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image151.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image155.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image156.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image157.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 26px; width: 262px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image158.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now L.H.S. = <img decoding=\"async\" style=\"height: 50px; width: 279px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image159.png\" \/>\u00a0\u00a0\u00a0 \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\">R.H.S. = <img decoding=\"async\" style=\"height: 49px; width: 226px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image160.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image161.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image162.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0From eq. (i) and (ii), we get<\/p>\n<p style=\"text-align: justify;\">L.H.S. = R.H.S.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 30px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image163.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-3\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_If_A_show_that_A2_%E2%80%93_5A_7I_0_Hence_find\"><\/span><strong>13. If A = <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image164.png\" \/><\/strong><strong>, show that A<sup>2<\/sup> \u2013 5A + 7I = 0. Hence find <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image165.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: A = <img decoding=\"async\" style=\"height: 49px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image166.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image167.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image166.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image166.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image168.png\" \/><\/p>\n<p style=\"text-align: justify;\">L.H.S. = <img decoding=\"async\" style=\"height: 25px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image169.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 202px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image170.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 198px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image171.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 178px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image172.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image173.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 208px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image174.png\" \/><\/p>\n<p style=\"text-align: justify;\">= R.H.S.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image175.png\" \/>\u00a0\u2026\u2026(i)<\/p>\n<p style=\"text-align: justify;\">To find: <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>, multiplying eq. (i) by <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image176.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image177.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image178.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image179.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image180.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image181.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/><img decoding=\"async\" style=\"height: 49px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image182.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-4\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_For_the_matrix_A_find_numbers_and_such_that\"><\/span><strong>14. For the matrix A = <\/strong><strong><img decoding=\"async\" style=\"height: 49px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image183.png\" \/><\/strong><strong>\u00a0find numbers <\/strong><strong><img decoding=\"async\" style=\"height: 15px; width: 14px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image184.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 19px; width: 14px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image185.png\" \/><\/strong><strong>\u00a0such that <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image186.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: A = <img decoding=\"async\" style=\"height: 49px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image187.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image188.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image189.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image190.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image191.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image192.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 252px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image193.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 215px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image194.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0We have <img decoding=\"async\" style=\"height: 19px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image195.png\" \/> \u2026\u2026\u2026.(i)<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 19px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image196.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image197.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image198.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here <img decoding=\"async\" style=\"height: 19px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image198.png\" \/>\u00a0satisfies <img decoding=\"async\" style=\"height: 19px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image199.png\" \/>\u00a0also, therefore\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image198.png\" \/><\/p>\n<p style=\"text-align: justify;\">Putting <img decoding=\"async\" style=\"height: 19px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image198.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 19px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image200.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image201.png\" \/>\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/> <img decoding=\"async\" style=\"height: 19px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image202.png\" \/><\/p>\n<p style=\"text-align: justify;\">Here also <img decoding=\"async\" style=\"height: 19px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image202.png\" \/>\u00a0satisfies <img decoding=\"async\" style=\"height: 19px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image203.png\" \/>\u00a0, therefore\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image202.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, <img decoding=\"async\" style=\"height: 19px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image198.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 34px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image202.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-5\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_For_the_matrix_A_show_that_Hence_find\"><\/span><strong>15. For the matrix A = <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image204.png\" \/><\/strong><strong>, show that <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image205.png\" \/><\/strong><strong>\u00a0Hence find <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image165.png\" \/><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: A = <img decoding=\"async\" style=\"height: 75px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image206.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image207.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 247px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image208.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 110px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image209.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 75px; width: 285px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image210.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 288px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image211.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image212.png\" \/><\/p>\n<p style=\"text-align: justify;\">L.H.S. = <img decoding=\"async\" style=\"height: 21px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image213.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 457px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image214.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 464px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image215.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 381px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image216.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 213px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image217.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image218.png\" \/>\u00a0= R.H.S.<\/p>\n<p style=\"text-align: justify;\">Now,\u00a0\u00a0 to find <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>, multiplying <img decoding=\"async\" style=\"height: 21px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image219.png\" \/>\u00a0by <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 273px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image220.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image221.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image222.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 359px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image223.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 350px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image224.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 274px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image225.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image226.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image227.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-6\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_If_A_verify_that_and_hence_find\"><\/span><strong>16. If A = <\/strong><strong><img decoding=\"async\" style=\"height: 75px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image228.png\" \/><\/strong><strong>, verify that <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 150px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image229.png\" \/><\/strong><strong>\u00a0and hence find <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image165.png\" \/><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Given: A = <img decoding=\"async\" style=\"height: 75px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image230.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 235px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image231.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 271px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image232.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image233.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now <img decoding=\"async\" style=\"height: 75px; width: 283px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image234.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 274px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image235.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image236.png\" \/><\/p>\n<p style=\"text-align: justify;\">L.H.S. = <img decoding=\"async\" style=\"height: 21px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image237.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 457px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image238.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 461px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image239.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 404px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image240.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 268px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image241.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image218.png\" \/>\u00a0= R.H.S.<\/p>\n<p style=\"text-align: justify;\">Now,\u00a0\u00a0 to find <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/>, multiplying <img decoding=\"async\" style=\"height: 21px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image237.png\" \/>\u00a0by <img decoding=\"async\" style=\"height: 20px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image060.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 268px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image242.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image243.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image244.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 360px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image245.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 350px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image246.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 303px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image247.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 75px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image248.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 75px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image249.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-7\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"17_Let_A_be_a_non-singular_matrix_of_order_3_x_3_Then_is_equal_to\"><\/span><strong>17. Let A be a non-singular matrix of order 3 x 3. Then <\/strong><strong><img decoding=\"async\" style=\"height: 26px; width: 50px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image250.png\" \/><\/strong><strong>\u00a0is equal to:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(A) <\/strong><img decoding=\"async\" style=\"height: 26px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image251.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <\/strong><img decoding=\"async\" style=\"height: 30px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image252.png\" \/><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <\/strong><img decoding=\"async\" style=\"height: 30px; width: 26px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image253.png\" \/><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <\/strong><img decoding=\"async\" style=\"height: 26px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image254.png\" \/><strong>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>If A is a non-singular matrix of order <img decoding=\"async\" style=\"height: 17px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image255.png\" \/>\u00a0then <img decoding=\"async\" style=\"height: 30px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image256.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0Putting <img decoding=\"async\" style=\"height: 21px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image257.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 30px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image258.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, option (B) is correct.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-8\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"18_If_A_is_an_invertible_matrix_of_order_2_then_det_is_equal_to\"><\/span><strong>18. If A is an invertible matrix of order 2, then det <\/strong><strong><img decoding=\"async\" style=\"height: 30px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image259.png\" \/><\/strong><strong>\u00a0is equal to:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(A) det A\u00a0 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <\/strong><img decoding=\"async\" style=\"height: 41px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image260.png\" \/><strong>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) 1\u00a0\u00a0 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) 0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Since <img decoding=\"async\" style=\"height: 20px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image261.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 14px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image005.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 30px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image262.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 30px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image263.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image003.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 46px; width: 70px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex4.5\/image264.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, option (B) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_45-9\"><\/span>NCERT Solutions class 12 Maths Exercise 4.5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Class_12\"><\/span>CBSE App for Class 12<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Exercise 4.5 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 4.5\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-4-5\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 4.5\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4552","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Exercise 4.5 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 4.5 in PDF format for free download. 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