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Question
If |A| = 3 and \[A^{- 1} = \begin{bmatrix}3 & - 1 \\ - \frac{5}{3} & \frac{2}{3}\end{bmatrix}\] , then write the adj A .
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Solution
|A| = 3 and \[A^{- 1} = \begin{bmatrix}3 & - 1 \\ - \frac{5}{3} & \frac{2}{3}\end{bmatrix}\]
\[A^{- 1} = \frac{1}{\left| A \right|}\left( adj A \right)\]
\[ \Rightarrow adj A = \left| A \right| A^{- 1}\]
adj A = 3
\[\begin{bmatrix}3 & - 1 \\ - \frac{5}{3} & \frac{2}{3}\end{bmatrix}\] = \[\begin{bmatrix}9 & - 3 \\ - 5 & 2\end{bmatrix}\]
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