If
\[
A=
\begin{bmatrix}
\cos\alpha& 0 &\sin\alpha\\
0& 1& 0
-\sin\alpha& 0 &\cos\alpha\\
\end{bmatrix}
\]
and \(A^2=A^T\) for one value of \(\alpha\in(0,\pi)\), then \(A^3=\):
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Whenever a matrix is orthogonal, replace \(A^T\) by \(A^{-1}\). This usually simplifies the problem immediately.