Prove or disprove: if $A$ is nonzero $2 \times 2$ matrix such that $A^2+A=0$, then A is invertible 
if $A$ is nonzero $2 \times 2$ matrix such that $A^2+A=0$, then A is invertible

I really can't figure it out. I know it's true but don't know how to prove it

This is not true. For example
$$
A=\begin{pmatrix}
-1&0\\
0&0
\end{pmatrix}
$$
