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प्रश्न
What is \[A^{-1}\] when \[|A|=9\] and \[\operatorname{adj}A=\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]?
पर्याय
\[9\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]
\[\frac19\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]
\[-\frac19\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]
\[\frac1{9}\begin{bmatrix}1&1&1\\0&1&3\\1&-2&1\end{bmatrix}\]
MCQ
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उत्तर
The inverse formula is \[A^{-1}=\frac1{|A|}\operatorname{adj}(A).\] Since \(|A|=9\), every entry of \(\operatorname{adj}A\) is multiplied by \(\frac19\).
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