If two invertible matrices A and B commute, then A^-1 and B^-1 must commute as well ??

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If two invertible matrices A and B commute, so their inverse must commute as well or not ?

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This follows from \begin{equation} A^{-1}B^{-1} = (BA)^{-1} = (AB)^{-1} = B^{-1}A^{-1}. \end{equation}