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If a matrix $A$ is such that $3 A^3+2 A^2+5 A+I=0$, then its inverse is
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Verified Answer
The correct answer is:
$-\left(3 A^2+2 A+5 I\right)$
$3 A^3+2 A^2+5 A+I=0 \Rightarrow I=-3 A^3-2 A^2-5 A$
$\Rightarrow I A^{-1}=-3 A^2-2 A-5 I$
$A^{-1}=-\left(3 A^2+2 A+5 I\right)$
$\Rightarrow I A^{-1}=-3 A^2-2 A-5 I$
$A^{-1}=-\left(3 A^2+2 A+5 I\right)$
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