If a matrix A is such that 3 A^3 + 2 A^2 + 5A + I = 0, then its i… - Vidyadip

MCQ

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

✓
$ - (3{A^2} + 2A + 5I)$
B
$3{A^2} + 2A + 5I$
C
$3{A^2} - 2A - 5I$
D
None of these

✓

Answer

Correct option: A.

$ - (3{A^2} + 2A + 5I)$

a
(a) $3{A^3} + 2{A^2} + 5A + I = 0 $

$\Rightarrow I = - 3{A^3} - 2{A^2} - 5A$

$ \Rightarrow $$I{A^{ - 1}} = - 3{A^2} - 2A - 5I$

$ \Rightarrow $ ${A^{ - 1}} = - (3{A^2} + 2A + 5I)$

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