We know that $A^{23} = 0$. What are the eigenvalues of $A$? 
Let $A$ be an $n \times n$ matrix. We know that $A^{23} = 0$. What are the eigenvalues of $A$?

I think it's just $0$, but I'm not sure. How should I do this problem?

Let $\lambda \in \mathbb{R}$ be an eigenvalue of $A$. Let $x \in \mathbb{R}^n$ be a corresponding eigenvector. Then
$$Ax = \lambda x \quad \Rightarrow \quad \lambda^{23}x = A^{23}x = 0x = 0.$$
Since $x \neq 0$, $\lambda^{23} = 0$ and thus $\lambda = 0$.
