Browse Questions

If a matrix A is such that $3A^3+2A^2+5A+I=0$ then its inverse is

$\begin{array}{1 1}(A)\;-(3A^2+2A+5I)&(B)\;3A^2+2A+5I\\(C)\;3A^2-2A-5I&(D)\;\text{None of these}\end{array}$

Can you answer this question?

$3A^3+2A^2+5A+I=0$
$I=-3A^3+2A^2+5A+I=0$
$IA^{-1}=-3A^2-2A-5I$
$A^{-1}=-(3A^2+2A+5I)$
Hence (A) is the correct answer.
answered Apr 23, 2014