If \( A=\left[\begin{array}{cc}\cos \theta & i \sin \theta \\ i \sin \theta & \cos \theta\end{array}\right],\lef…

If \( A=\left[\begin{array}{cc}\cos \theta & i \sin \theta \\ i \sin \theta & \cos \theta\end{array}\right],\left(\theta=\frac{\pi}{24}\right) \) and \( A^{5}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \) where \( \mathrm{i}=\sqrt{-1} \), then which one of the following is not true?

[JEE Main 2020, 4 Sep (Shift 1)]