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Let A and B are square matrices of order 3 such that A B 2 = B A and B A 2 = A B . If A B 3 = A 3 B m , then m is equal to

Options

  1. A3
  2. B4
  3. C5
  4. D7

Correct answer

D. 7

Step-by-step solution

A B 3 = A B A B A B = A B A B A B = A A B 2 A B 2 B = A 2 B B A B 3 = A 2 B A B 2 B 3 = A 2 B A B 5 = A 2 A B 2 B 5 = A 3 B 7

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