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Install NowNCERT Solutions class 12 Maths Exercise 4.2 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

**Using the properties of determinants and without expanding in Exercise 1 to 5, prove that:**

**1. **

**Ans. **Given:

Operating

0 = 0 [ C_{1} and C_{2} are identical]

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

**2. **

**Ans. **On Operating

=

= = 0 = R.H.S.

[ All entries of one column here first are zero]

**3. **

**Ans. **On operating

= =

= 9 x 0 = 0 [ two columns are identical] Proved.

**4. **

**Ans. **Given: =

Operating

=

= = 0 [ two columns are identical] Proved.

**5. **

**Ans. **L.H.S. = operating

=

=

=

= [operating ]

= [operating ]

= [operating ]

= [Interchanging and ]

= [Interchanging and ]

= = R.H.S.

**6. **

**Ans. **Let

= [Taking common from each row]

Interchanging rows and columns in the determinants on R.H.S.,

Proved.

**7. **

**Ans. **L.H.S. =

Taking common from respectively,

=

= [operating ]

= =

= = = R.H.S.

**8. (i) **

**(ii) **

**Ans. (i) **L.H.S. = operating and ,

=

= [Expanding along 1^{st} column]

=

=

= = = R.H.S. Proved.

**(ii) **L.H.S. = operating and

=

=

=

=

=

=

=

=

=

= = R.H.S.

**9. **

**Ans. **

L.H.S. = = [Multiplying by respectively]

= =

= [operating ]

=

=

=

=

=

=

=

=

=

=

= = R.H.S.

**10. (i) **

**(ii) **

**Ans. (i) **L.H.S. =

=

=

= [operating and ]

=

= = R.H.S.

**(ii) **L.H.S. =

=

=

= [operating and ]

=

= =

= R.H.S. Proved.

**11. (i) **

**(ii) **

**Ans. (i)** L.H.S. =

=

=

=

=

=

= = R.H.S. Proved.

**(ii)** L.H.S. =

=

=

=

=

=

= = R.H.S. Proved.

**12. **

**Ans. **L.H.S. =

=

=

=

=

=

=

=

=

=

=

= = R.H.S. Proved.

**13. **

**Ans. **L.H.S. =

=

=

=

=

=

= = R.H.S.

**14. **

**Ans. **L.H.S. =

Multiplying by respectively and then dividing the determinant by

=

=

=

=

=

=

= = R.H.S. Proved.

### NCERT Solutions class 12 Maths Exercise 4.2

**Choose the correct answer in Exercises 15 and 16.**

**15. Let A be a square matrix of order 3 x 3, then is equal to:**

**(A) **

**(B) **

**(C) **

**(D) **

**Ans. **Let A = be a square matrix of order 3 x 3. ……….(i)

= [From eq. (i)]

Therefore, option (C) is correct.

### NCERT Solutions class 12 Maths Exercise 4.2

**16. Which is the following is correct:**

**(A) Determinant is a square matrix.**

**(B) Determinant is a number associated to a matrix.**

**(C) Determinant is a number associated to a square matrix.**

**(D) None of these.**

**Ans. **Since, Determinant is a number associated to a square matrix.

Therefore, option (C) is correct.

## NCERT Solutions class 12 Maths Exercise 4.2

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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