I am trying to prove this problem and I am having trouble were to exactly start. The question is:
Show that if $A$ is any matrix, then $K = A^T A$ and $L = AA^T$ are both symmetric matrices.
My attempt:
In order to be symmetric then $A=A^T$ then $K = AA$ and since by definition we have that $K = A^n$ is symmetric since $n > 0$.