Question 1006565
A matrix is <a href = "https://en.wikipedia.org/wiki/Symmetric_matrix">symmetric</a> if and only if it is equal to its transpose, ie
X = X^T


Given:
A = A^T (since matrix A is symmetric)
B = B^T (matrix B is symmetric)
AB = BA


We want to prove:
AB is symmetric
ie, AB = (AB)^T



AB = BA
AB = B^T*A^T ... use the given info above
AB = (AB)^T ... use <a href="https://en.wikipedia.org/wiki/Transpose">property 3</a>


So the claim has been proven true. AB is indeed symmetric.