Question

If adj $A=\left[\begin{array}{cc}2& 3\\ 4& -1\end{array}\right]\mathrm{and}\mathrm{adj}B=\left[\begin{array}{cc}1& -2\\ -3& 1\end{array}\right]$, find adj AB.

Answer 1

Given:

$$\begin{gathered} adjA=\left[\begin{array}{cc}2& 3\\ 4& -1\end{array}\right] \\ adjB=\left[\begin{array}{cc}1& -2\\ -3& 1\end{array}\right] \end{gathered}$$

For any two non-singular matrices,

$$\begin{gathered} adj\left(AB\right)=\left(adjB\right)\times \left(adjA\right) \\ \Rightarrow adj\left(AB\right)=\left[\begin{array}{cc}-6& 5\\ -2& -10\end{array}\right] \end{gathered}$$