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# Class 12 NCERT Solutions- Mathematics Part I – Chapter 4 Determinants- Exercise 4.2 | Set 2

### (ii) Solution:

(i) L.H.S.=   ∵ L.H.S.=R.H.S

Hence proved

(ii)   ∵ L.H.S.=R.H.S

Hence proved

### Question 12. Solution:  ∵ L.H.S.=R.H.S

Hence proved

### Question 13. Solution:   ∵ L.H.S.=R.H.S

Hence proved

### Question 14. Solution: Multiplying column1,column2,column3  by  a,b,c respectively and then dividing the determinant by  a,b,c .  ∵ L.H.S.=R.H.S

Hence proved

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

(A) k|A|

(B) k2|A|

(C) k3|A|

(D) 3k|A|

Solution:

Let A = be a square matrix of order 3 x 3   ….(1)

Now, kA= ⇒|kA|= ⇒|kA|=k3 ∴ |kA|= k3|A|            [ from eqn .(1) ]

∴ option (C) is correct.

### Question 16.Which of 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

Solution:

Since, Determinant is a number which is always associated to a square matrix.

∴ option (C) is correct.

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