I wonder if the hypothesis in the title is true. And if so, some ideas to prove it. I know $(A^T)^{-1} = (A^{-1})^T$
EDIT: Edited the title to match the generic answer. T does not have to be triangular.
2026-03-31 05:35:49.1774935349
$(T^{-1})^i == (T^i)^{-1}$?
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$T^k(T^{-1})^k = T\cdot T \cdot ... T \cdot T^{-1} \cdot T^{-1} \cdot ... T^{-1} = I$, thus $(T^{k})^{-1} = (T^{-1})^{k}$ if I understand the question correctly