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  • Explain solution rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 28

Explain solution rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 28

Answers (1)

option (d) none of these

Given: 3 A^{3}+2A^{2}+5A+I=0

Hint: use simple calculation to get the result.

\begin{aligned} &\text { Solution: } 3 A^{3}+2 A^{2}+5 A=-I \\ &A\left(3 A^{2}+2 A+5 I\right)=-I \\ &3 A^{2}+2 A+5 I=-A^{-1}\left(\text { multiply } A^{-1}\right. \text { on both sides) } \\ &\Rightarrow A^{-1}=-\left(3 A^{2}+2 A+5 I\right) \end{aligned}

Hence, option (d) is correct

 

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