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MHT CET202617 April 2026Morning ShiftMathematicsMatricesActual

If A is a non-singular matrix and A^2 - A + I = 0 , then A⁻¹ =

Options

  1. AA
  2. BA - I
  3. CI - A
  4. DA + I

Correct answer

C. I - A

Step-by-step solution

Given A^2 - A + I = 0 Multiplying both sides by A⁻¹ , we get A⁻¹(A^2 - A + I) = 0 A - I + A⁻¹ = 0 A⁻¹ = I - A Answer: I - A

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