\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A \in \mathrm{GL}_n(\mathbb{K})\) and \(B \in M_n(\mathbb{K})\) such that \(A B = B A\). Show that \(A^{-1} B = B A^{-1}\).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.