若对矩阵 $A =\left(\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & 1 \\ 2 & -1 & 1\end{array}\right)$ 施以初等列变换得矩阵 $B =\left(\begin{array}{ccc}-1 & -2 & -1 \\ 2 & 2 & 2 \\ 0 & -2 & 0\end{array}\right)$, 求满足 $A P = B$ 的所有可逆矩阵 $P$.
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