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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Determinants
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If $A^2-A+I=0$ then the inverse of A is

$(a)\;A+I\qquad(b)\;A\qquad(c)\;A-I\qquad(d)\;I-A$

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1 Answer

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$A^2-A+I=0$
Multiply $A^{-1}$ on both sides
$A^{-1}A^2-A^{-1}A+A^{-1}I=A^{-1}0$
$\Rightarrow A-1+A^{-1}=0$
$\Rightarrow A^{-1}=1-A$
Hence (d) is the correct answer.
answered Nov 21, 2013 by sreemathi.v
 

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