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If A ≠ B , A B = B A and A 2 = B 2 , then the value of the determinant of matrix A + B is (where A and B are square matrices of order 3 × 3 )

Options

  1. A0
  2. B1
  3. C3 3
  4. D3 2

Correct answer

A. 0

Step-by-step solution

A 2 - B 2 = A - B A + B = 0 given   A B = B A Since, A ≠ B ⇒ A - B is not a null matrix Hence, A + B is a null matrix or d e t A - B = d e t A + B = 0 In both cases d e t A + B = 0

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