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MHT CET20228 Aug 2022Morning ShiftMathematicsMatricesActual

If A= [ array cc 2 & -1 -1 & 2 array ] such that A^2-4 A+3 I=0 , where I is a unit matrix of order 2 , then A⁻¹ is

Options

  1. A1 3 [ array cc -2 & 1 1 & -2 array ]
  2. B1 3 [ array cc 2 & -1 -1 & 2 array ]
  3. C1 3 [ array ll 2 & 1 1 & 2 array ]
  4. D1 3 [ array cc -1 & 2 2 & -1 array ]

Correct answer

C. 1 3 [ array ll 2 & 1 1 & 2 array ]

Step-by-step solution

aligned & A^2-4 A+3 I=0 A(4 I-A)=3 I A ( 4 I-A 3 )=I & A⁻¹= 4 I-A 3 = 1 3 [ array ll 2 & 1 1 & 2 array ] [ as A A⁻¹=I ] aligned

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