If $A^3-2A^2-A+2I=O$, then $A$ is equal to If $A^3-2A^2-A+2I=O$, then $A$ is equal to
$(A) I$ $(B) 2I$ $(C)\begin{bmatrix} 2  & -1 & 2 \\-1 & 0 & 0 \\\ 0 & 1 & 0
\end{bmatrix}$ $(D)\begin{bmatrix} 2  & 1 & -2 \\1 & 0 & 0 \\\ 0 & 1 & 0
\end{bmatrix}$
My Attempt:
$A^3-2A^2-A+2I=O$
$A^2(A-2I)-I(A-2I)=O$
$(A^2-I)(A-2I)=O$
Either $(A^2-I)=O$ or  $(A-2I)=O$
I got $A=I$ or $A=-I$ or $A=2I$ but the correct answers are (A), (B), (C), (D).
Please help.

The eignevalues of $C,D$ are $\pm1,2$ with the characteristic equation is:
$x^3-2x^2-x+2=0$. The eigenvalues of $A,B$ are $1$'s which also obey this equation, so they are all possible answers.
