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If A and B are non-singular square matrix of same order 3 × 3 , then which of the following options is correct?

Options

  1. Aa d j ( A B ) = A B
  2. B( a d j A B ) - 1 = a d j ( A B )
  3. Ca d j ( A B ) - 1 = ( a d j A B ) - 1
  4. Da d j ( A B ) T = A B - 2

Correct answer

C. a d j ( A B ) - 1 = ( a d j A B ) - 1

Step-by-step solution

a d j ( A B ) = A B 2 ( a d j A B ) - 1 = a d j A B - 1 a d j ( A B ) - 1 = ( A B ) - 1 2 = A B - 2 a d j ( A B ) - 1 = a d j A B - 1 = A B 2 - 1 = A B - 2 a d j ( A B ) T = ( A B ) T 2 = A B 2

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