IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 5
IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Matrices, with the answer and a step-by-step solution.
If
then, for a positive integer n, Aⁿ equals:
- A
- B
- C
- D
Answer & solution
Answer: Option B
Compute the first few powers and look for the pattern.
A² = A × A has top-right entry 1×2 + 2×1 = 4, and the other entries stay 1, 0, 1.
So A² is the matrix with rows (1, 4) and (0, 1).
A³ likewise gives top-right 1×2 + 2×1 applied again, producing 6.
The pattern is that only the top-right entry grows, by 2 each time, giving 2n for Aⁿ.
This can be proved by induction: if Aⁿ has rows (1, 2n) and (0, 1), then multiplying by A gives top-right 1×2 + 2n×1 = 2(n + 1), which is the same form with n replaced by n + 1.
So Aⁿ has rows (1, 2n) and (0, 1).
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