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Matrix Theory - Isometries

Find the eigenvalues and eigenvectors of A.
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I will use t instead of theta, it is easier to write; to find the eigenvalues we need to solve Det(A-xI)=0, which means:
(cost-x)(-cost-x)-sint*sint=0 so:
x^2=1 (using that the cos^2+sin^2=1).
So x1=1 and x2=-1 are the eigenvalues.
In what follows we will assume sint non-zero. If sint is zero, we discuss in the end of the proof what the answer is.
Eigenvectors for ...

Solution Summary

This shows how to find eigenvalues and eigenvectors.