5. Let $A = \begin{bmatrix} 0 & 0 & -2 \\ 1 & 2 & 1 \\ 1 & 0 & 3 \end{bmatrix}$, please express $A^3$ as $PDP^{-1}$ with D a diagonal matrix and P an invertible matrix.
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5. Let $A = \begin{bmatrix} 0 & 0 & -2 \\ 1 & 2 & 1 \\ 1 & 0 & 3 \end{bmatrix}$, please express $A^3$ as $PDP^{-1}$ with D a diagonal matrix and P an invertible matrix.