Question

If A and B are symmetric matrices of order n (A ≠ B), then

(A) A + B is skew-symmetric

(B) A + B is symmetric

(C) A + B is a diagonal matrix

(D) A + B is a zero matrix

Answer 1

Answer is (B) A + B is symmetric

A and B are symmetric. A = A′, B = B′. So

(A + B)′ = A′ + B′ = A + B