I've A^-1 = - A What is A
I've figured that A^2= -I but what's then?
Let $\displaystyle A= \begin{bmatrix}a & b \\ c & d\end{bmatrix}$. Then $\displaystyle A^2= \begin{bmatrix}a^2+ bd & ab+ bd \\ ac+ cd & bc+ d^2\end{bmatrix}= \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$. So we must have $\displaystyle a^2+ bd= 1$, $\displaystyle ab+ bd= 0$, $\displaystyle ac+ cd= 0$, and $\displaystyle bc+ d^2= 1$. You might try things like taking b (or c) equal to 0 or not equal to 0 and see what you get.