Let$ A$ and $X$ be invertible complex matrices such that $XAX^{−1} = A^2$ . Prove that there exists a natural number m such that each eigenvalue of A is an m-th root of unity.
i was taking the set $\{ \lambda , \lambda^1 , \lambda^{2} , \lambda^{3}, \dots, \lambda^{m} \}$
$\lambda$ is the eigenvalue of $ A$
I don't know how to show that there exists a natural number m such that each eigenvalue of A is an m-th root of unity.
Pliz help me
Thanks in advance