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If A, B and C are square matrices of order 3 and det ( BC )=2 det ( ~A ) , then what is the value of det (2 ~A ⁻¹ BC ) ?

Options

  1. A16
  2. B8
  3. C4
  4. D2

Correct answer

A. 16

Step-by-step solution

Given |B C|=2|A| Now, |2 ~A ⁻¹ BC |=2^3 | ~A ⁻¹ || BC |=8 1 | ~A | 2| ~A |=16

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