Skew-symmetry of matrix $C = AB - BA$

Question

Matrices $A$ and $B$ are skew-symmetric and $C = AB - BA$. Show $C$ is also skew-symmetric.

I see $\mbox{tr}(C)=0$ and $C = AB - (AB)^T$, but nothing else.

Answer 1

$C^* = B^* A^* - A^* B^*=(-B)(-A)-(-A)(-B) =BA-AB=-C$.