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

The answer becomes evident, when you view it in terms of the minimal polynomial.
Now given the above equation A^2 + A = 0, this can also be written as A(A+I) = 0
Since A is not 0, 
A either has A+I = 0, i.e, A = -I. (when A+I is the minimal polynomial of A)
  or has A(A+I) = 0 as its minimal polynomial, in this case the eigenvalues of A are 0 and 1, which implies the determinant of A = 0.
Hence its not invertible.
So either A = -I or A is not invertible.
