Q.If $A = \begin{pmatrix} \cos \theta & -\sin \theta \ \sin \theta & \cos \theta \end{pmatrix}$ , then $A^{100} + A^{99} + \cdots + A + I$ equals

\dfrac{\sin 50.5 \theta}{\sin 0.5 \theta} A

\dfrac{\sin 50 \theta}{\sin \theta} I

\dfrac{\sin 50.5 \theta}{\sin 0.5 \theta} I

101 I

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.If A=(cos⁡θ−sin⁡θ sin⁡θcos⁡θ)A = \begin{pmatrix} \cos \theta & -\sin \theta \ \sin \theta & \cos \theta \end{pmatrix}A=(cosθ​−sinθ sinθ​cosθ​), then A100+A99+⋯+A+IA^{100} + A^{99} + \cdots + A + IA100+A99+⋯+A+I equals