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JEE Main20208 Jan 2020Evening ShiftMathematicsMatricesActual

If A = 2 2 9 4 and I = 1 0 0 1 , then 10   A - 1 , is equal to.

Options

  1. AA - 4 I
  2. B6 I - A
  3. CA - 6 I
  4. D4 I - A

Correct answer

C. A - 6 I

Step-by-step solution

Characteristics equation of matrix A is A - x I = 0 . 2 2 9 4 - x 1 0 0 1 = 0 ⇒ 2 - x 9 2 4 - x = 0   ⇒ x 2 - 6 x - 10 = 0 ∴ A 2 - 6 A - 10 I = 0 10 A - 1 = A - 6 I .

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