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  4. If A2-A+I=O, then the inverse of the matrix A is

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Q. If $A^{2}-A+I=O$, then the inverse of the matrix $A$ is

WBJEEWBJEE 2009Matrices

Solution:

Given, $A^{2}-A+I=O$
$\Rightarrow A^{2}-A=-I$
$\Rightarrow A^{2}A^{-1}-AA^{-1}=-IA^{-1}$
$\Rightarrow A-I=-A^{-1}$
$\Rightarrow A^{-1}=I-A$