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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 \( A^{5}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] \)
P
WV
where \( \mathrm{i}=\sqrt{-1} \), then which one of the following is not true?
[JEE Main-2020 (September)]
(a) \( \mathrm{a}^{2}-\mathrm{b}^{2}=\sqrt{-1} \)
(b) \( \mathrm{a}^{2}-\mathrm{c}^{2}=1 \)
(c) \( \mathrm{a}^{2}-\mathrm{d}^{2}=0 \)
(d) \( 0 \leq \mathrm{a}^{2}+\mathrm{b}^{2} \leq 1 \)
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