Q. If $A^{3} = O$, then $I + A + A^{2}$ eauals
A) $I - A$
B) $\left( I + A^{1} \right)^{- 1}$
C) $(I - A)^{- 1}$
D) None of these
Explanation
(c)
Given
$A^{3} = 0$
Now,
$(I - A)\left( I + A + A^{2} \right)$
$= I^{2} + IA + IA^{2} - AI - A^{2} - A^{3}$
$= I - A^{3}$
$= I$
$\Rightarrow (I - A)^{- 1} = I + A + A^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.