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For the following two (02) items: Let A = pmatrix & - & pmatrix . What is [ adj , A]⁻¹ equal to?

Options

  1. A-A
  2. B-A^T
  3. CA
  4. DA^T

Correct answer

C. A

Step-by-step solution

Given A = pmatrix & - & pmatrix The determinant of A is |A| = ^2 - (- )( ) = ^2 + ^2 = 1 For any non-singular matrix, the inverse is given by A⁻¹ = 1 |A| adj , A Substituting |A| = 1 , we get adj , A = A⁻¹ Taking the inverse on both sides yields [ adj , A]⁻¹ = (A⁻¹)⁻¹ = A Answer: A

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