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JEE Main202228 Jun 2022Morning ShiftMathematicsMatricesActual

Let A be a matrix of order 3 × 3 and det A = 2 . Then det det ( A ) adj 5 adj A 3 is equal to _____.

Options

  1. A256 × 10 6
  2. B1024 × 10 6
  3. C512 × 10 6
  4. D256 × 10 11

Correct answer

C. 512 × 10 6

Step-by-step solution

(|( det ( A )) adj (5 adj ( A ))| ) (= |2 adj (5 adj ( A ^3 ) ) | ) (=2^3 adj (5 adj ( A ^3 ) | . ) (=2^3 |5 adj ( A ^3 ) |^2 ) (=2^3 (5^3 | adj ( A ^3 ) | )^2 ) (=2^3 5^6 | adj A ^3 |^2 ) (=2^3 5^6 ( (| ~A |^3 )^2 )^2 ) (=2^3 5^6 2¹²=2¹⁵ 5^6 ) (=2^9 10^6 ) (=512 10^6 )

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