Find the eigenvalues and eigenvectors of A.
See attached file for full problem description.
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:
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 ...
This shows how to find eigenvalues and eigenvectors.