$A^2=-I_4$. Find possible values of minimal polynomial and characteristic polynomial Let $A\in\mathbb{R}^{4\times 4}$ satisfy $$A^2=-I_4 .$$

(a) Find possible values of $m_a$ (minimal polynomial) and $p_a$ (characteristic polynomial).
(b) Find an example for A satisfying the condition.

Please help me approach the first question. I can assume (b) would immediately follow.

We have
$$
A^2 = -I\\
A^2 +I = 0
$$
and we direclty read off the polynomial $f(x) = x^2 + 1$, with $f(A) = 0$. Now you just need to figure out how the minimal and characteristic polynomials both relate to any given polynomial where $A$ is a root.
