To prove two matrices are similar 
$\overline A$ denotes the conjugate of the matrix $A\in M_n(\mathbb C)$. Prove $\overline AA$ is similar to $A\overline A$.

I am reviewing my summer homework. I have a proof but it is long, so I posted this question to seek some more straightforward approaches. My idea is to show $\overline AA$ and $A\overline A$ have the same Jordan blocks.

Your idea is working, but is not so easy to put it in practice. Maybe this reference can help you.
