Linear Algebra Hermitian Proof

Can anyone please help me understand this problem? I'm confused as to how to prove this, here is the problem:

Let A and B be Hermitian matrices. Show that AB = BA if and only if AB is Hermitian.

Let A* denote the conjugate transpose of A.

Since A and B are Hermitian, we know that A* = A and B* = B.
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So, AB is Hermitian
<==> (AB)* = AB
<==> B* A* = AB
<==> BA = AB, since A = A* and B = B*.

I hope this helps!