Let $A \in \mathbb{R}^{2 \times 2}$ be a D6160: Real square matrix such that

(i)	\begin{equation} A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \end{equation}

Result R5505: Cofactor matrix for a 2-by-2 real square matrix shows that \begin{equation} \text{Cof} A = \begin{bmatrix} d & - c \\ - b & a \end{bmatrix} \end{equation} Therefore \begin{equation} \text{Adj} A = (\text{Cof} A)^T = \begin{bmatrix} d & - b \\ - c & a \end{bmatrix} \end{equation} $\square$