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MHT CET202211 Aug 2022Morning ShiftMathematicsMatricesActual

If A is non-singular matrix of order 3 such that (A-2 I )(A-4 I )=0 , then 1 6 A+ 4 3 A⁻¹ is (where I is a unit matrix of order 3 and 0 is a null matrix of order 3)

Options

  1. A6I
  2. BI
  3. C0
  4. D2I

Correct answer

B. I

Step-by-step solution

aligned & (A-2 I )(A-4 I )=0 & A^2-6 A+8 I =0 & A^2+8 I =6 A & A^2 A⁻¹+8 I A⁻¹=6 A A⁻¹ & A+8 A⁻¹=6 I & 1 6 A+ 4 3 A⁻¹= I aligned

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