Prove that if $M$ is antisymmetric, then $M^2$ is
I have no idea where to begin. I tried to diagonalise the matrix and attempt something with $D^2 = S^T M^2 S$, but I don’t really know what I can do with this information, especially since I don’t have information about the eigenvalues of $M$. Could someone help me proceed from here? Thanks!