Solve for $X$
$$ A^{-1} \, X \, B-B=-A^{-1} \, X $$
$$ A = \begin{bmatrix}1&-1\\1&2\end{bmatrix} \quad B = \begin{bmatrix}-1&1\\2&1\end{bmatrix} $$
Solve for $X$
$$ A^{-1} \, X \, B-B=-A^{-1} \, X $$
$$ A = \begin{bmatrix}1&-1\\1&2\end{bmatrix} \quad B = \begin{bmatrix}-1&1\\2&1\end{bmatrix} $$
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$$A^{-1}XB-B=-A^{-1}X \\XB-AB=-X \\ X(B+I)=AB \\ X=(AB)(B+I)^{-1}$$