$A$ is a square matrix with $A^2 - 3A + I = O$. What is $A^{-1}$?

Explanation

1. 01

   Move $I$ across: $3A - A^2 = I$, that is $A(3I - A) = I$.

2. 02

   $(3I - A)A = I$ in the same way, so $A^{-1} = 3I - A$.