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Let A and B be matrices of order 3 3 . If |A|= 1 2 2 and |B|= 1 729 , then what is the value of 2 ~B ( adj (3 ~A ) ?

Options

  1. A27
  2. B27 2 2
  3. C27 2
  4. D1

Correct answer

D. 1

Step-by-step solution

aligned |2 ~B [ adj (3 ~A )]| & =|2 ~B | adj (3 ~A ) = & 2^3| ~B ||3 ~A |³⁻¹ = & 8| ~B | (3^3| ~A | )^2 = & 8| ~B | 3^6| ~A |^2 = & 8 1 729 3^6 ( 1 2 2 )^2 = & 8 1 729 729 1 8 =1 aligned

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