We know that if $A$ is an orthogonal matrix then $A^{-1}=A^t$ and so $$\det(A)=\pm 1.$$ Put of curiosity, is there a set of conditions that can be added to $A$ such that $\det(A)=1$?
2026-04-01 13:42:45.1775050965
Quick question about the determinant of an orthogonal matrix
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