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AP EAMCET202422 May 2024Morning ShiftMathematicsMatricesActual

If P and Q are two 3 3 matrices such that |P Q|=1 and |P|=9 , then the determinant of adjoint the matrix P . Adj 3 Q is

Options

  1. A9^4
  2. B1 9^4
  3. C9^2
  4. D1 9^2

Correct answer

A. 9^4

Step-by-step solution

aligned & |P||Q|=1 |Q|= 1 9 & adj (P adj (3 Q)|=| adj adj (3 Q)|| adj P & =|3 Q|^4|P|^2= (3^3 )^4 |Q|^4|P|^2 & =3¹² 1 9^4 9^2= 3¹² 3^4 =3^8=9^4 . aligned

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