Question

Write the adjoint of the matrix $A=\left[\begin{array}{cc}-3& 4\\ 7& -2\end{array}\right].$

Answer 1

$$\begin{gathered} \mathrm{Let}{C}_{ij}\mathrm{be}\mathrm{a}\mathrm{cofactor}\mathrm{of}{a}_{ij}\mathrm{in}A. \\ \mathrm{Now}, \\ {C}_{11}=-2 \\ {C}_{12}=-7 \\ {C}_{21}=-4 \\ {C}_{22}=-3 \\ \therefore adjA={\left[\begin{array}{cc}-2& -7\\ -4& -3\end{array}\right]}^T=\left[\begin{array}{cc}-2& -4\\ -7& -3\end{array}\right] \end{gathered}$$