Eigenvalues of matrice. I need help with the following. If $1$ is an eigenvalue of $A^2$ , $A$ is a $2 \times 2$ matrix, then $1$ is an eigenvalue of $A$. If $A$ is a reflective matrix, then $A^2 = I$.

If $1$ is an eigenvalue of $A^2$, then $1$ and(!) $-1$ are possible eigenvalues of $A$.

Example: $A=-I_2$. $-1$ is an eigenvalue of $A$, $1$ is not an eigenvalue of $A$.