# NCERT Solutions for Class 12 Maths Exercise 3.3

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## NCERT Solutions for Class 12 Maths Exercise 3.3

### Matrics Solutions

#### Q 2) Ifthen verify that:

(i) (A + B)’ = A’ + B’
(ii) (A – B)’ = A’ – B’

#### Q 3) Ifthen verify that:

(i) (A + B)’ = A’ + B’
(ii)  (A – B)’ = A’ – B’

#### Q 6) (i) If A =then verify that A’A = I.

(ii) If A = then verify that A’A = I.

#### Q 7) (i) Show that the matrix A =is a symmetric matrix.

(ii) Show that the matrix A = is a skew symmetric matrix.

#### Q 8) For a matrix A =verify that:

(i) (A + A’) is a symmetric matrix.
(ii) (A – A’) is a skew symmetric matrix.

#### Q 11) If A and B are symmetric matrices of same order, AB – BA is a:

(A) Skew-symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix

Given: A and B are symmetric matrices ∴ A = A’ and B = B’
Now, (AB – BA)’ = (AB)’ – (BA)’  ∴ (AB – BA)’ = B’A’ – A’B’ [Reversal law]

∴ (AB – BA)’ = BA – AB [From eq. (i)] ∴ (AB – BA)’ = – (AB – BA)
∴  (AB – BA) is a skew matrix.

Therefore, option (A) is correct.

(A) π/6
(B) π/3
(C) π
(D) 3π/2