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Explain solution rd sharma class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 29

Answers (1)

option (b) \frac{1}{det(A)}

Given – A is an invertible matrix

Hint – you must know about invertible matrix concept

Solution –

We know that AA^{-1}=I

\begin{aligned} &\Rightarrow\left|\mathrm{AA}^{-1}\right|=|\mathrm{I}| \\ &\Rightarrow|\mathrm{A}|\left|\mathrm{A}^{-1}\right|=1 \\ &\Rightarrow\left|A^{-1}\right|=|A|^{-1} \end{aligned}

Hence, is option (b) is correct

 

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