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  4. If A3=0 , then I+A+A2 equals

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Q. If $A^{3}=0$ , then $I+A+A^{2}$ equals

NTA AbhyasNTA Abhyas 2022

Solution:

Consider $I^{3}-A^{3}=\left(\right.I-A\left.\right)\left(\right.I^{2}+IA+A^{2}\left.\right)=\left(\right.I-A\left.\right)\left(\right.I+A+A^{2}\left.\right)$
$\Rightarrow I=\left(\right.I-A\left.\right)\left(\right.I+A+A^{2}\left.\right)$
$\Rightarrow \left(\right.I+A+A^{2}\left.\right)=\left(\right. I - A \left.\right)^{- 1}$