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JEE Main2017MathematicsMatricesActual

Let A be any 3 × 3 invertible matrix. Then which one of the following is not always true?

Options

  1. Aa d j a d j (A) = A 2 . a d j (A) - 1
  2. Ba d j a d j (A) = A . a d j (A) - 1
  3. Ca d j a d j (A) = A . A
  4. Da d j (A) = A . A - 1

Correct answer

B. a d j a d j (A) = A . a d j (A) - 1

Step-by-step solution

∵ A - 1 = 1 A a d j A ∴ a d j a d j A = a d j A a d j A - 1 = A 2 a d j A - 1 … … i ∵ A a d j A = A I ∴ a d j A = A A - 1 ∴ a d j A - 1 = 1 A A ∴ from (i) a d j a d j A = A . A

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