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Let A be a 3 × 3 matrix such that adj A = 2 - 1 1 - 1 0 2 1 - 2 - 1 and B = adj a d j A . If | A | = λ and B - 1 ⊤ = μ , then the ordered pair λ , μ is equal to

Options

  1. A3 ,   1 81
  2. B9 ,   1 9
  3. C3 ,   81
  4. D9 ,   1 81

Correct answer

A. 3 ,   1 81

Step-by-step solution

a d j   A = A 2 = 9 ⇒ A = ± 3 = λ ⇒ λ = 3 ⇒ B = a d j   A 2 = 81 ⇒ B - 1 T = B - 1 = B - 1 = 1 B = 1 81 = μ ∴ λ ,   μ = 3 ,   1 81 .

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