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If AA ^ T = I then identify the correct statement -

Options

  1. AA ^ T ( A - I ₃ )=- ( A - I ₃ )^ T
  2. BA is always invertible
  3. Cdet (A-I₃ )=0
  4. DA is singular

Correct answer

B. A is always invertible

Step-by-step solution

aligned & - ( A - I ₃ )^ T =- ( A - AA ^ T )^ T =- ( A ^ T - A ^ T A )=- A ^ T & ( I - A )= A ^ T ( A - I ) & Also. AA ^ T = I | A |^2= I | A |= 1 aligned

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