If \( A(\theta)=\left(\begin{array}{cc}\sin \theta & i \cos \theta ...

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If \( A(\theta)=\left(\begin{array}{cc}\sin \theta & i \cos \theta \\ i \cos \theta & \sin \theta\end{array}\right) \), then
(a) \( A(\theta) \) is invertible for all \( \theta \in \mathbf{R} \)
(b) \( A(\theta)^{-1}=A(-\theta) \)
(c) \( A(\theta)^{-1}=A(\pi-\theta) \)
(d) \( A(\theta)+A(\pi+\theta) \) is a null matrix
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