This is a question from my friend.
It should be easy. But I have no knowledge about complex matrix.
Let $A,K$ be two invertible complex n-by-n matrices satisfying the following conditions: A' = A^{-1}=\bar{A}\mbox{ and } \bar{K} = AK\bar{A},
where A' for transpose, $\bar{A}$ for the conjugate, and $A^{-1}$ for the inverse.
Prove that $K$ is a real matrix.