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

2527 242 WBJEEWBJEE 2009Matrices Report Error

A

$A - I$

18%

B

$I - A$

43%

C

$A + I$

26%

D

$A$

13%

Solution:

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