Question

Find the adjoint of the given matrix.

$\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

Answer 1

Let $\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$
$A_{11}=4,A_{12}=-3,A_{21}=-2and{A}_{22}=1$
$a_{dj}A={\left[\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right]}^T={\left[\begin{array}{cc}4& -3\\ -2& 1\end{array}\right]}^T=\left[\begin{array}{cc}4& -2\\ -3& 1\end{array}\right]$