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 eigen values 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.