Question

If A and B are symmetric matrices of the same order, then

(A) AB is a symmetric matrix

(B) A - B is skew-symmetric matrix

(C) AB + BA is a symmetric matrix

(D) AB - BA is a symmetric matrix

Answer 1

Answer is (C) AB + BA is a symmetric matrix

A and B are symmetric matrices of same order, i.e. A = A′, B = B′.

Then (AB + BA)^T = (AB)^T + (BA)^T

= B^T × A^T + A^T × B^T = BA + AB = AB + BA

So, AB + BA is a symmetric matrix.