Directions (Q. No. 11 and 12) Choose the correct answer in the following questions:

11. If A, B are symmetric matrices of same order, then AB-BA is a

(i) Skew-symmetric matrix

(ii) Symmetric matrix

(iii) Zero matrix

(iv) Identity matrix

11. If A, B are symmetric matrices of same order, then AB-BA is a

(i) Skew-symmetric matrix

(ii) Symmetric matrix

(iii) Zero matrix

(iv) Identity matrix

Sol. Given, a and B are symmetric matrices

→ A’ = A and B’ = B

(AB – BA)’ = (AB)’ – (BA)’ [∵ (A-B)’ = A’ – B’]

= B’A’ – A’B’ [∵ (AB)’ = B’A’]

= BA – AB [∵ A’ = A and B’ = B]

= -(AB-BA) → (AB-BA)’ = -(AB-BA)

Thus, (AB-BA) is a skew symmetric matrix. So, correct option is (a)

→ A’ = A and B’ = B

(AB – BA)’ = (AB)’ – (BA)’ [∵ (A-B)’ = A’ – B’]

= B’A’ – A’B’ [∵ (AB)’ = B’A’]

= BA – AB [∵ A’ = A and B’ = B]

= -(AB-BA) → (AB-BA)’ = -(AB-BA)

Thus, (AB-BA) is a skew symmetric matrix. So, correct option is (a)