设三阶矩阵 $\boldsymbol{A}, \boldsymbol{B}$ 满足 $\boldsymbol{A}^2 \boldsymbol{B}-\boldsymbol{A}-\boldsymbol{B}=\boldsymbol{E}$, 若 $\boldsymbol{A}=\left(\begin{array}{rrr}1 & 0 & 1 \\ 0 & 2 & 0 \\ -2 & 0 & 1\end{array}\right)$, 求 $\boldsymbol{B} $
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