Thread: 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.

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,