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JEE Main20241 Feb 2024Morning ShiftMathematicsMatricesActual

If A = 2 1 − 1 2 , B 1 0 1 1 , C = A B A T and X = A T C 2 A , then det X is equal to:

Options

  1. A243
  2. B729
  3. C27
  4. D891

Correct answer

B. 729

Step-by-step solution

Given: A = 2 1 - 1 2 ⇒ A = 2 + 1 = 3 B = 1 0 1 1 ⇒ B = 1 And C = A B A T ⇒ C = A B A T ⇒ C = A 2 B as A = A T ⇒ C = 9 Now, solving X = A C 2 A T . ⇒ X = A C 2 A T ⇒ X = 3 × 9 2 × 3 ⇒ X = 729

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