(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let l be an eigenvalue of an orthogonal matrix A, where l = r + is. Prove that l * conj(l) = r^2 + s^2 = 1.

2. Relevant equations

3. The attempt at a solution

I am really confused on where to go with this one.

I have Ax = A I x = A A^T A x = l^3 x

and Ax = l x so l x = l^3 x

l = l^3

l^2 = 1

l = 1 or -1

But I can't really figure out what to do from here, am I even on the right track?

Thanks for the help

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# Homework Help: Orthogonal Matrix

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