\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that for every \(A \in \mathrm{GL}_n(\mathbb{K})\), the matrix \(A^2\) is invertible and \((A^2)^{-1} = (A^{-1})^2\).
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