If A = 1 & 0 \\ 1 & 1 and I = 1 & 0 \\ 0 & 1 , then which one of the following holds for all n ≥ 1 ? - Mathematics MCQ AIEEE 2026 | ExamTest.live

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If A = [1101] and I = [1001], then which one of the following holds for all n \geq 1 ?

Solution & Step-by-step Explanation

Let's calculate the first few powers of A : A = [1101] A^{2} = [1101] [1101] = [1201] A^{3} = A^{2} \cdot A = [1201] [1101] = [1301] By observation, A^{n} = [1 n 01] .Now check Option A: n A - (n - 1) I : n A = [n n 0 n] (n - 1) I = [n - 1 0 0 n - 1] n A - (n - 1) I = [n - (n - 1) n - 0 0 n - (n - 1)] = [1 n 01] This matches A^{n} . Thus, Option A is correct.

Try it yourself before checking the explanation above.

If A = [1101] and I = [1001], then which one of the following holds for all n \geq 1 ?

A^{n} = n A - (n - 1) I

A^{n} = 2^{n - 1} A - (n - 1) I

A^{n} = n A + (n - 1) I

A^{n} = 2^{n - 1} A + (n - 1) I

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