If $A$ and $B$ are orthogonal matrices and they have same odd row, prove that one of matrices $A+B$ and $A-B$ are singular.
I have no idea, can you help me? I tried with $\det(A+B)(A-B)=\det(A^2-AB+BA-B^2)$, but I do not get anything.
2026-05-05 07:38:03.1777966683
If matrices $A$ and $B$ are orthogonal then $A-B$ or $A+B$ are singular
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