Proving that 2 matrix's are symmetrical

Let A be a m x n matrix. Show that A^t A and AA^t are both symmetric.


If you guys could help me out and show what you did, it would be amazingly awesome. Thanks in advance.

Recall that C is symmetric iff C^t = C.
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1) Note that
(A^t A)^t
= A^t (A^t)^t, since (AB)^t = B^t A^t
= A^t A, since (A^t)^t = A.

Hence, A^t A is symmetric.

2) Similarly, AA^t is symmetric (same argument as above).

I hope this helps!