设 $\boldsymbol{A} \boldsymbol{P}=\boldsymbol{P} \boldsymbol{\Lambda}$, 其中 $\boldsymbol{P}=\left(\begin{array}{rrr}1 & 1 & 1 \\ 1 & 0 & -2 \\ 1 & -1 & 1\end{array}\right), \boldsymbol{\Lambda}=\left(\begin{array}{lll}-1 & & \\ & 1 & \\ & & 5\end{array}\right)$,求 $\varphi(\boldsymbol{A})=\boldsymbol{A}^8\left(5 \boldsymbol{E}-6 \boldsymbol{A}+\boldsymbol{A}^2\right)$.
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