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If B , C are square matrices of same order such that C 2 = B C - C B and B 2 = - I , where I is an identity matrix, then the inverse of matrix C - B is

Options

  1. AC
  2. BC + B
  3. CC - B
  4. DI

Correct answer

B. C + B

Step-by-step solution

Given, C 2 - B C + C B = 0 ⇒ C 2 - B C + C B - B 2 + B 2 = 0 ⇒ C - B C + B + B 2 = 0 ⇒ C - B C + B = I (as B 2 = - I ) Hence, C - B - 1 = C + B

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