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NDA2023MathematicsDeterminantsActual

The value of the determinant of a matrix A of order 3 is 3 . If C is the matrix of cofactors of the matrix A , then what is the value of determinant of C ^2 ?

Options

  1. A3
  2. B9
  3. C81
  4. D729

Correct answer

C. 81

Step-by-step solution

Given |A|=3, ( . where . A _ 3 3 ) Since, C=( adj (A))^ Now, | C |=| adj A |=| A |^ n -1 =3^2=9 So, |C^2 |=9^2=81

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