1. Tardigrade
  2. Question
  3. Mathematics
  4. If A2 - A + I = 0 , then the inverse of A is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $A^2 - A + I = 0$ , then the inverse of A is

Determinants

Solution:

Given $A^2 - A + I = 0$
$A^{-1} A^2 - A^{-1} A + A^{-1}.I = A^{-1}.0$
(Multiplying $A^{-1}$ on both sides)
$\Rightarrow \, A -1+ A^{-1} = 0$ or $A^{-1} = I - A$.