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Provide solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 13

Answers (1)

:  option (a) A2

Given:  A^{3}=I

Hint: to find A-1,  multiple both side by A-1

Solutions:

A^{3}=I

Post multiplying by A-1  both sides

\begin{aligned} &A^{3} \cdot A^{-1}=\mathrm{I} \cdot A^{-1} \\ &A^{2} \cdot A \cdot A^{-1}=\mathrm{I} \cdot A^{-1} \\ &A^{2} \cdot \mathrm{I}=A^{-1} \quad\left(\therefore A A^{-1}=\mathrm{I}\right) \\ &\Rightarrow A^{-1}=A^{2} \end{aligned}

Hence, option (a) is correct

 

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