I know that all permutation matrices $A$ satisfy $A^T=A^{-1}$, but is the converse, all matrices $A$ with $A^T=A^{-1}$ are permutation matrices, also true? I believe it is true, but I haven't been able to confirm it. I know this is probably a very dumb question, but I'm very unsure and just want some clarification.
2026-03-26 17:30:28.1774546228
Are all matrices $A$ with $A^T=A^{-1}$ permutation matrices?
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