If A and B are symmetric matrices, then AB is symmetric if and only if A and B commute .i.e.
AB = (AB)^T = B^TA^T = BA

[∵ B^T = B and A^T = A]

Question

If A and B are symmetric matrices, then write the condition for which AB is also symmetric.

Philoid · Accepted Answer

If A and B are symmetric matrices, then AB is symmetric if and only if A and B commute .i.e.

AB = (AB)^T = B^TA^T = BA

[∵ B^T = B and A^T = A]