First slide

Applications of determinant

Question

If square matrix A is such that $3 A^{3} + 2 A^{2} + 5 A + I = O$ , then $A^{- 1}$ is equal to

Moderate

A

$3 A^{2} + 2 A + 5 I$
B

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

$3 A^{2} - 2 A - 5 I$
D

none of these

Solution

We have $A (3 A^{2} + 2 A + 5 I) = - I$
$∴ A^{- 1} = - (3 A^{2} + 2 A + 5 I)$ [ $∴$ Inverse of a matrix is unique]

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