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.
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Originally Posted by Jskid 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 Spoiler: You sure you want to look so soon? Spoiler: Fine, do it Spoiler: Isn't it true that is real orthogonal if and only if ? So that ?
A "tiny" alternative: is orthogonal iff So,
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