Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

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)

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

Posted by

Vakul

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 session 2 paper 2 answer key objection window closes today; fees
anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year

Latest Question