Can someone please clarify for me these two statements.
Let $A$ of order ($n\times n$) be a matrix over $\Bbb R$. $A^{4} = I$. so:
- $A$ diagonalizable over $\Bbb R$.
- $A$ diagonalizable over $\Bbb C$.
The only statement I know is concerning eigenvalues: if $a$ is an eigenvalue of $A$ then $a^{4}$ is an eigenvalue of $A^{4}$.