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Matrices
Question
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If A2 – A + I = 0, then the inverse of A is

  • A + I

  • A

  • A – I

  • I – A

Answer

D.

I – A

Given A2 – A + I = 0
A–1A2 – A–1A + 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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