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

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

Grade:12

2 Answers

Latika Leekha
askIITians Faculty 165 Points
9 years ago
Given that A2 – A + I = 0
If we multiply both sides by A-1 we have,
A-1 (A2 – A + I) = A-1 .0 = 0
Hence, A – I + A-1 = 0
This gives A-1 = -(A – I)
= I – A.
Thanks & Regards
Latika Leekha
askIITians Faculty
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

Given that A2 – A + I = 0
If we multiply both sides by A-1 we have,
= A^-1 (A2 – A + I)
= A-1 .0
= 0
Hence, A – I + A-1 = 0
This gives A-1 = -(A – I)
= I – A.

Thanks and Regards

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