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If for any 2 2 square matrix A , A( adj A)= [ array ll 8 & 0 0 & 8 array ] , then the value of det (A) .

Options

  1. A6
  2. B5
  3. C7
  4. D8

Correct answer

D. 8

Step-by-step solution

For any square matrix A of order n , the fundamental property involving the adjoint matrix is A( adj A) = ( det A) I_n , where I_n is the identity matrix of order n . Given that A is a 2 2 matrix, n = 2 . Therefore, I₂ = bmatrix 1 & 0 0 & 1 bmatrix . The given equation is A( adj A) = bmatrix 8 & 0 0 & 8 bmatrix . Substituting the property into the given equation, we have ( det A) bmatrix 1 & 0 0 & 1 bmatrix = bmatrix 8 & 0 0 & 8 bmatrix . Comparing the matrices, we get ( det A) = 8 . Answer: 8

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