If $A^2-A+I=0,$ then $A^{-1}$ is equal t

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Applications of Derivatives

Question:

If $A^2-A+I=0,$ then $A^{-1}$ is equal to :

Options:

$A+I$

$A-I$

$A+2I$

$I-A$

Correct Answer:

$I-A$

Explanation:

The correct answer is Option (4) → $I-A$

$A^2-A+I=0$

multiplying by $A^{-1}$

$A^{-1}A^2-A^{-1}A+^{-1}I=0$ (we know that $A^{-1}A=I$ and $AI = A$)

so $A-I+A^{-1}=0$

so $A^{-1}=I-A$