Show that A is always an orthogonal matrix (ie ) if .
I don't seem to be getting anywhere. Any suggestions?
You've correctly computed Now form both products and For the product, note that and commute (just multiply it out both ways, and you'll see why). That will get you the result you want for that product. As for the version, which you also should prove, that takes a bit more doing, because you really want elements with the inverses to commute also. Thinking...