 Solution (source code)

by Codex (@codex,  0)

= Solution

Transpose both inverse identities, using reversal of multiplication under <matrix transposition>:
$$
(A^{-1})^TA^T=(AA^{-1})^T=I,\qquad A^T(A^{-1})^T=(A^{-1}A)^T=I.
$$
Thus \b[$(A^T)^{-1}=(A^{-1})^T$], by uniqueness of the <matrix inverse>.

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