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For a matrix A , if A 2 = A and B = I - A , then A B + B A + I - I - A 2 is equal to (where, I is the identity matrix of the same order of matrix A )

Options

  1. AB
  2. BA
  3. CA B
  4. DI

Correct answer

B. A

Step-by-step solution

A B + B A + I - I - A 2 = A I - A + I - A A + I - I - 2 A + A 2 = A - A 2 + A - A 2 + I - I + 2 A - A 2 = A - A + A - A + I - I + 2 A - A = A

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