If matrix A = [a(i,j)] is a 2 × 2 matrix such that a(i,j) = 1 for i ≠ j and a(i,j) = 0 for i = j, then A² is: A. A B. I C. O D. 2I Answer: B) I Explanation: Based on the rule, A = [[0, 1], [1, 0]]. A² = [[0, 1], [1, 0]] × [[0, 1], [1, 0]] = [[1, 0], [0, 1]], which is the identity matrix I.

imo class 12 matrices

If matrix A = [a(i,j)] is a 2 × 2 matrix such that a(i,j) = 1 for i ≠ j and a(i,j) = 0 for i = j, then A² is:

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If matrix A = [a(i,j)] is a 2 × 2 matrix such that a(i,j) = 1 for i ≠ j and a(i,j) = 0 for i = j, then A² is:

A. A
B. I
C. O
D. 2I

Answer: B) I

Explanation: Based on the rule, A = [[0, 1], [1, 0]]. A² = [[0, 1], [1, 0]] × [[0, 1], [1, 0]] = [[1, 0], [0, 1]], which is the identity matrix I.

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