设 $\boldsymbol{A}=\left(\begin{array}{lll}1 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 0\end{array}\right), \boldsymbol{B}=\left(\begin{array}{lll}1 & 1 & 0 \\ 1 & 2 & 2 \\ 0 & 0 & 1\end{array}\right), 3$ 阶方阵 $\boldsymbol{X}, \boldsymbol{Y}$ 满足

$$
A X B^{-1}-A Y B^{-1}=E, X Y-Y^2=E .
$$


其中 $\boldsymbol{E}$ 为 3 阶单位矩阵，求 $\boldsymbol{Y}$ ．