Eigenvalues of $A$ with $A^3 = A$ I just got a quick practice question here that I think should be simple but I can't find a definitive answer.

Let $A$ be a square matrix such that $A^3 = A$. What can you say about the eigenvalues of $A$?

It is multiple choice and all of the answers are combinations of $-1$, $1$, and $0$. I'm pretty sure $0$ and $1$ are possible but I'm not sure how to prove any of them. Thanks in advance.

Minimal polynomial of matrix $A$ satisfying $A^3=A$ is given by $x^3-x=0$,so the possible eigenvalues will be $0,1,-1$, depending on the given matrix now, we can select it from MCQ.
