If $A$ is a square matrix that satisfies $A^2-A+2I=0$, show that $A+I$ is invertible If $A$ is a square matrix that satisfies $A^2-A+2I=0$, show that $A+I$ is invertible. I understand how to find if $A$ is invertible but I don't know how to solve for the $A+I$ version.

name $$  B = A + I \; , \; $$
$$ A = B - I $$
given
$$ A^2 - A + 2I = 0  $$
$$ (B-I)^2 - (B-I) + 2 I = 0  $$
$$ B^2 - 2 B + I - B + I + 2I = 0  $$
$$ B^2 - 3 B + 4 I = 0 $$
