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Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices1 Mark
Question
If for a square matrix $A, A^2-A+I=0$, then $A^{-1}$ equals
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Answer

We have, $A^2-A+I=O$
Pre$-$multiplying with $A^{-1}$ on both sides, we get
$\left(A^{-1} A\right) \cdot A-A^{-1} \cdot A+A^{-1} \cdot I=A^{-1} \cdot O$
$\Rightarrow I \cdot A-I+A^{-1}=O$
$\Rightarrow A^{-1}=-(A-I)=I-A$

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