If A= bmatrix 1 & a 0 & 1 bmatrix where a N , then what is A^ 100 -A^ 50 -2A^ 25 equal to, where I is the identity matrix?

NDA 2021 Mathematics question

where , then what is

equal to, where is the identity matrix?

Answer: (A)

, and, by induction, . Therefore

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Question ID VK-033622