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Let A be a matrix of order 3 3 and | A |=4 . If |2 adj (3 ~A )|=2^ a 3^ b , then what is the value of ( + ) ?

Options

  1. A12
  2. B13
  3. C17
  4. D24

Correct answer

B. 13

Step-by-step solution

|2 adj (3 A)|=2^3 | adj (3 A)| [ order of matrix =3]=2^3 |3 A|³⁻¹=2^3 |3 A|^2=2^3 (3^3 )^2(|A|)^2=2^3 3^6 |A|^2=2^3 3^6 4^2=2^3 3^6 2^4=2^7 3^6 =7, =6 + =13

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