Let $A=\left[\begin{array}{cc}3 & -1 \\ 2 & 4\end{array}\right]$, then adjoint (A) is:

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

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

here finding cofactors

so C₁₁ = 4     C₁₂ = -2

C₂₁ = 1     C₂₂ = 3

so  Adj A = $\left[\begin{array}{ll}c_{11} & c_{12} \\ c_{21} & c_{22}\end{array}\right]^{T}=\left[\begin{array}{cc}4 & -2 \\ 1 & 3\end{array}\right]^{T}$

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