is orthogonal iff . So, if are orthogonal then, which implies orthogonal.
I'm not sure how to do this. I tried making two general 2 x 2 matricies like so:
To be orthogonal, these equations must be satisfied (via dot product):
ab + cd = 0
ef + gh = 0
Multiplying the two matricies, and then finding the dot product of the result yeilds:
The best I could do was show that:
I think I'm attempting this wrong. :/ Any advice?