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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.

**Download NCERT solutions for Determinants as PDF**

## NCERT Solutions class 12 Maths Determinants

**Find adjoint of each of the matrices in Exercise 1 and 2.**

**1. **** **

**Ans. **Here A =

A_{11} = Cofactor of

A_{12} = Cofactor of

A_{21} = Cofactor of

A_{22} = Cofactor of

adj. A = =

**2. **** **

**Ans. **Here A =

=

adj. A =

**Verify A (adj. A) = **** in Exercise 3 and 4.**

**3. **** **

**Ans. **Let A =

adj. A =

A.(adj. A) =

= = …..(i)

Again (adj. A). A =

= = …..(ii)

And =

Again …..(iii)

From eq. (i), (ii) and (iii) A. (adj. A) = (adj. A). A =

**4. **** **

**Ans. **Let A =

=

adj. A =

A. (adj. A) =

=

= ……….(i)

Again (adj. A). A =

=

= ……….(ii)

And

=

Also = ……….(iii)

From eq. (i), (ii) and (iii) A. (adj. A) = (adj. A). A =

### NCERT Solutions class 12 Maths Exercise 4.5

**Find the inverse of the matrix (if it exists) given in Exercise 5 to 11.**

**5. **** **

**Ans. **Let A =

= 0

Matrix A is non-singular and hence exist.

Now adj. A = And

**6. **** **

**Ans. **Let A =

=

Matrix A is non-singular and hence exist.

Now adj. A = And

**7. **** **

**Ans. **Let A =

=

exists.

A_{11} = , A_{12} = ,

A_{13} = , A_{21} = ,

A_{22} = , A_{23} = ,

A_{31} = , A_{32} = ,

A_{33} =

adj. A =

**8. **** **

**Ans. **Let A =

=

exists.

A_{11} = , A_{12} = ,

A_{13} = , A_{21} = ,

A_{22} = , A_{23} = ,

A_{31} = , A_{32} = ,

A_{33} =

adj. A =

**9. **** **

**Ans. **Let A =

=

exists.

A_{11} = , A_{12} = ,

A_{13} = , A_{21} = ,

A_{22} = , A_{23} = ,

A_{31} = , A_{32} = ,

A_{33} =

adj. A =

**10. **** **

**Ans. **Let A =

=

exists.

A_{11} = , A_{12} = ,

A_{13} = , A_{21} = ,

A_{22} = , A_{23} = ,

A_{31} = , A_{32} = ,

A_{33} =

adj. A =

**11. **** **

**Ans. **Let A =

=

exists.

A_{11} = ,

A_{12} = , A_{13} = ,

A_{21} = , A_{22} = ,

A_{23} = , A_{31} = ,

A_{32} = , A_{33} =

adj. A =

### NCERT Solutions class 12 Maths Exercise 4.5

**12. Let A = **** and B = **** verify that **** **

**Ans. **Given: Matrix A =

= 15 – 14 = 1 0

=

Matrix B =

= 54 – 56 = 0

Now AB = = =

=

Now L.H.S. = ……….(i)

R.H.S. =

=

= ……….(ii)

From eq. (i) and (ii), we get

L.H.S. = R.H.S.

### NCERT Solutions class 12 Maths Exercise 4.5

**13. If A = ****, show that A**^{2} – 5A + 7I = 0. Hence find ** **

^{2}– 5A + 7I = 0. Hence find

**Ans. **Given: A =

L.H.S. =

=

=

=

=

=

= R.H.S.

……(i)

To find: , multiplying eq. (i) by .

=

= =

### NCERT Solutions class 12 Maths Exercise 4.5

**14. For the matrix A = **** find numbers **** and **** such that **** **

**Ans. **Given: A =

We have ……….(i)

Here satisfies also, therefore

Putting in eq. (i),

Here also satisfies , therefore

Therefore, and

### NCERT Solutions class 12 Maths Exercise 4.5

**15. For the matrix A = ****, show that **** Hence find **

**Ans. **Given: A =

=

Now

=

=

L.H.S. =

=

=

=

= = = R.H.S.

Now, to find , multiplying by

=

### NCERT Solutions class 12 Maths Exercise 4.5

**16. If A = ****, verify that **** and hence find **

**Ans. **Given: A =

=

Now

=

=

L.H.S. =

=

=

=

= = = R.H.S.

Now, to find , multiplying by

=

### 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:**

**(A) **

**(B) **** **

**(C) **** **

**(D) **** **

**Ans. **If A is a non-singular matrix of order then

Putting

Therefore, option (B) is correct.

### NCERT Solutions class 12 Maths Exercise 4.5

**18. If A is an invertible matrix of order 2, then det **** is equal to:**

**(A) det A **

**(B) **** **

**(C) 1 **

**(D) 0**

**Ans. **Since

Therefore, option (B) is correct.

## NCERT Solutions class 12 Maths Exercise 4.5

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

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Very nice solution it is helpful for the students