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

  • Option 1)

    A

  • Option 2)

    A+I

  • Option 3)

    I-A

  • Option 4)

    A-I

 

Answers (2)
V Vakul

As we learnt in 

Property of inverse of a matrix -

Every invertible matrix possesses a unique inverse 

-

 

 A^{2}-A+I=0

A^{2}A^{-1}-AA^{-1}+IA^{-1}=0

A(AA^{-1})-I+A^{-1}=0

AI-I+A^{-1}=0

\therefore A^{-1}=I-IA

So, A^{-1}=I-IA=I-A

 

 


Option 1)

A

Incorrect option

Option 2)

A+I

Incorrect option

Option 3)

I-A

Correct option

Option 4)

A-I

Incorrect option

N neha

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