If A^3=O, then A^2+A+I= - Vidyadip

MCQ

If $A^3=O$, then $A^2+A+I=$

A
$I-A$
✓
$(I-A)^{-1}$
C
$(I+A)^{-1}$
D
$I+A$

✓

Answer

Correct option: B.

$(I-A)^{-1}$

(b) $: I-A^3=I \Rightarrow(I-A)\left(I+A+A^2\right)=I$
$\therefore \quad I+A+A^2=(I-A)^{-1}$.

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