If A=[\table 1 , a ; 0 , 1], where a \in \mathbb{N}, then what is A^{100}-A^{50}-2 A^{25} equal to? [NDA-II 2021]

I where I is the identity matrix.

UPSC NDA 2 2021 Mathematics Solved Paper

Question : 11 of 120

Marks: +1, -0

If A=[

1	a
0	1

], where a∈ℕ, then what is A100−A50−2A25 equal to?

[NDA-II 2021]

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1−1−2	100a−50a−50a
0−0−0	1−1−2

1	‌ na ‌
0	1

1	100a
0	1

1	50a
0	1

1	25a
0	1