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BITSAT2019MathematicsMatricesActual

If A is an 3 × 3 non- singular matrix, such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals to

Options

  1. AB - 1 '
  2. BI + B
  3. CI
  4. DB - 1

Correct answer

C. I

Step-by-step solution

Given, A A ' = A ' A and B = A - 1 A ' B B ' = A - 1 A ' A - 1 A ' ' = A - 1 A ' A ' ' A - 1 ' = A - 1 A ' A A ' - 1 ∵   A ' ' = A , A - 1 ' = A ' - 1 = A - 1 A ' A A ' - 1 = A - 1 A A ' A ' - 1 = A - 1 A A - 1 A ' = I · I = I

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