Solving for matrices $A$ and $B$

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$$A^{-1}B^{-1}A\,B=\begin{bmatrix}7&6\\2&1\end{bmatrix}$$

Is there a shortcut to solve for $A$ and $B$? Or is there a solution for $A$ and $B$ at all?

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Hint: Take the determinant of both sides.