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If A^2-A+I=0 , then the inverse of A is

Options

  1. AA+I
  2. BA
  3. CA-I
  4. DI-A

Correct answer

D. I-A

Step-by-step solution

Given A^2-A+I=0A⁻¹ A^2-A⁻¹ A+A⁻¹-I=A⁻¹ 0 (Multiplying A⁻¹ on both sides) A-I+A⁻¹=0 or A⁻¹=I-A

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