Solution
= Solution
In the orthonormal <basis> $(|G\rangle,|B\rangle)$, direct multiplication gives
$$
Q_M=\begin{pmatrix}\cos2\alpha&\sin2\alpha\\-\sin2\alpha&\cos2\alpha\end{pmatrix}
$$
(up to the equivalent opposite orientation convention).
= Solution
In the orthonormal <basis> $(|G\rangle,|B\rangle)$, direct multiplication gives
$$
Q_M=\begin{pmatrix}\cos2\alpha&\sin2\alpha\\-\sin2\alpha&\cos2\alpha\end{pmatrix}
$$
(up to the equivalent opposite orientation convention).