I'm not sure how to do this. I tried making two general 2 x 2 matricies like so:

$\displaystyle \[

A =

\begin{array}{cc}

a & b \\

c & d \\

\end{array}

\]$

$\displaystyle \[

B =

\left( {\begin{array}{cc}

e & f \\

g & h \\

\end{array} } \right)

\]$

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:

$\displaystyle a^2ef + b^2gh = 0$

$\displaystyle c^2ef + d^2gh = 0$

The best I could do was show that:

$\displaystyle (a^2 - c^2)(ef) = (b^2 - d^2)(ef)$

I think I'm attempting this wrong. :/ Any advice?