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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- Mar 30th 2011, 09:23 PMJskidorthogonal 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. - Mar 30th 2011, 09:25 PMDrexel28
- Mar 30th 2011, 09:55 PMFernandoRevilla
A "tiny" alternative:

$\displaystyle M\in\mathbb{R}^{n\times n}$ is orthogonal iff $\displaystyle MM^{t}=I$

So, $\displaystyle (AB)(AB)^t=\ldots =I$