If A = [[0, 1], [−1, 0]], then A⁴ is equal to: A. [[1, 0], [0, 1]] B. [[0, 0], [0, 0]] C. [[0, 1], [−1, 0]] D. [[−1, 0], [0, −1]] Answer: A) [[1, 0], [0, 1]] Explanation: A² = [[0, 1], [−1, 0]] × [[0, 1], [−1, 0]] = [[−1, 0], [0, −1]] = −I. Then A⁴ = (A²)² = (−I)² = I = [[1, 0], [0, 1]].

imo class 12 matrices

If A = [[0, 1], [−1, 0]], then A⁴ is equal to:

VAVidaara Admin Asked 6d ago 0 views 0 answers

If A = [[0, 1], [−1, 0]], then A⁴ is equal to:

Answer: A) [[1, 0], [0, 1]]

Explanation: A² = [[0, 1], [−1, 0]] × [[0, 1], [−1, 0]] = [[−1, 0], [0, −1]] = −I. Then A⁴ = (A²)² = (−I)² = I = [[1, 0], [0, 1]].