Question

If |A| = 3 and \[A^{- 1} = \begin{bmatrix}3 & - 1 \\ - \frac{5}{3} & \frac{2}{3}\end{bmatrix}\] , then write the adj A .

Answer 1

|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

\[\begin{bmatrix}3 & - 1 \\ - \frac{5}{3} & \frac{2}{3}\end{bmatrix}\] = \[\begin{bmatrix}9 & - 3 \\ - 5 & 2\end{bmatrix}\]