Show that if A and B are orthogonal matrices, then AB is an orthogonal matrix.
I think I need to show that the columns of A are orthonormal to each other, but I don't know how.
You often pick the hardest characterization to use. Try picking another one--solution below--use at your own risk
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You sure you want to look so soon?
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Fine, do it
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Isn't it true that $\displaystyle A$ is real orthogonal if and only if $\displaystyle A^{-1}=A^\top$? So that $\displaystyle (AB)^{-1}=B^{-1}A^{-1}=B^\top A^\top=(AB)^\top$?