If a matrix A satisfies the equaiton $A^3-6A^2+11A-6I=0$ then  $A^{-1}$ can be

$A^3-6A^2+11A-6I=0$
By verification A=I is roots of equation
$\begin{array}{l}(A-I)\left(A^2-5A+6I\right)=0\\ \Rightarrow (A-I)(A-2I)(A-3I)=0\\ \Rightarrow A^{-1}=I,\frac{1}{2}I,\frac{1}{3}I\end{array}$