[SOLVED] Symmetric Matrix Factorizations

Class notes and textbook skim this topic. Most internet resources are too complex for my current level of knowledge.

Need a little advice on how to approach the following problems.

What I know: Symmetric Matrix <=> A^T = A

The following statements produce a symmetric matrix assuming A^T = A, and B^T = B:

A^2 - B^2 True

(A - B)(A + B) False

ABA False

ABAB False

Did I get these all correct?

Therefore the product of two symmetric matrices isn't necessarily symmetric.

What would be some conditions where they would be symmetric?