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Let A and B be two square matrices of order 3 such that A = 3 and B = 2 , then the value of A - 1 ⋅ a d j B - 1 ⋅ a d j 2 A - 1 is equal to (where a d j ( M ) represents the adjoint matrix of M )

Options

  1. A72
  2. B64 27
  3. C8 9
  4. D16 27

Correct answer

D. 16 27

Step-by-step solution

A - 1 ⋅ a d j B - 1 ⋅ a d j 2 A - 1 = 1 A ⋅ B - 1 2 2 A - 1 2 = 1 A × 1 B 2 ⋅ 2 6 A 2 = 2 6 3 3 ⋅ 2 2 = 16 27

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