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AP EAMCET202421 May 2024Morning ShiftMathematicsMatricesActual

Let A be a 4 4 matrix and P be its adjoint matrix. If |P|= | A 2 | , then |A⁻¹ |=

Options

  1. A1 4
  2. B8
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

aligned & P = adj ( A ) & | P |=| adj ( A )|=| A |^ n-1 =| A |^3 & | P |= | A 2 |= 1 2^4 | ~A | & | A |^3= 1 2^4 | ~A | | A |^2= 1 16 | ~A |= 1 4 aligned | A ⁻¹ |= 1 | ~A | = 4

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