Q.If $A = \begin{pmatrix} 1 & 0 \ 0 & -1 \end{pmatrix}$ , then $A^{100} + A^{99} + \cdots + A + I$ equals

101 I

100 I

50 I

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

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Q.If A=(10 0−1)A = \begin{pmatrix} 1 & 0 \ 0 & -1 \end{pmatrix}A=(1​0 0​−1​), then A100+A99+⋯+A+IA^{100} + A^{99} + \cdots + A + IA100+A99+⋯+A+I equals