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Question
If adj \[A = \begin{bmatrix}2 & 3 \\ 4 & - 1\end{bmatrix}\text{ and adj }B = \begin{bmatrix}1 & - 2 \\ - 3 & 1\end{bmatrix}\]
Solution
Given: \[adj A = \begin{bmatrix}2 & 3 \\ 4 & - 1\end{bmatrix}\]
\[adj B = \begin{bmatrix}1 & - 2 \\ - 3 & 1\end{bmatrix}\]
For any two non-singular matrices, \[adj\left( AB \right) = \left( adj B \right) \times \left( adj A \right)\]
\[ \Rightarrow adj\left( AB \right) = \begin{bmatrix}- 6 & 5 \\ - 2 & - 10\end{bmatrix}\]
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