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Question: If A<sup>2</sup> – A + I = 0, then the inverse of A is –...

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

A

A + I

B

A

C

A – I

D

I – A

Answer

I – A

Explanation

Solution

A2 – A + I = 0

A–1(A2 – A + I) = 0

A2A–1 – A–1A + A–1I = 0

AI – I + A–1 = 0

A – I + A–1 = 0

A–1 = I – A