(a) Show that the Jones matrix of a polarization analyzer set at angle \(\alpha\) to the \(X\)-axis is given by

\[ \underline{\mathbf{L}}(\alpha)=\left[\begin{array}{cc} \cos ^{2} \alpha & \sin \alpha \cos \alpha \\ \sin \alpha \cos \alpha & \sin ^{2} \alpha \end{array}\right] \]

(b) Show that this matrix is not unitary.