Question

If matrix A and B are symmetric and AB = BA iff _________

(a) AB is symmetric matrix

(b) AB is an anti-symmetric matrix

(c) AB is a null matrix

(d) None of the mentioned

I got this question during an interview for a job.

This interesting question is from Transpose of Matrices in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Correct option is (a) AB is symmetric matrix

Explanation: For two symmetric matrices A and B, AB is a symmetric matrix if and only if AB = BA.