Q. Let $(x) = \ \frac{1 + x}{1 - x}$ . If $A$ is matrix for which $A^{3} = 0$, then $f(A)$ is
A) $I + A + A^{2}$
B) $I + 2A + A^{2}$
C) $I - A - A^{2}$
D) None of these
Explanation
(b)
$(I - A)f(A) = I + A$
$\Rightarrow f(A) = (I + A)(I - A)^{- 1}$
$= (I + A)\left( I + A + A^{2} \right)$
$= I + A + A^{2} + A + A^{2} + A^{3}$
$= I + 2A + 2A^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.