orthogonal matrices

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.

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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,