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BITSAT2024MathematicsMatricesActual

If A is a square matrix of order 3 , then Adj ( Adj .A^2 ) =

Options

  1. A|A|^2
  2. B|A|^4
  3. C|A|^8
  4. D| A |¹⁶

Correct answer

C. |A|^8

Step-by-step solution

| adj ( adj A^2 ) |=| adj A |=| A |^ n-1 =| A |^2 | adj A^2 |=| adj A|^2= (|A|^2 )^2=|A|^4 | adj ( adj A^2 ) |= (|A|^4 )³⁻¹= (|A|^4 )^2=|A|^8

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