Let $A \in \mathbb{C}^{2 \times 2}$ be a D6159: Complex square matrix such that

(ii)	$C_{i, j}$ is a D6183: Complex square matrix cofactor for $A$ with respect to $(i, j)$ for each $i, j \in \{ 1, 2 \}$

Let $i, j \in \{ 1, 2 \}$ each be a D5094: Positive integer.

Then

(1)	\begin{equation} i = j \quad \implies \quad A_{i, 1} C_{j, 1} + A_{i, 2} C_{j, 2} = \text{Det} A \end{equation}
(2)	\begin{equation} i = j \quad \implies \quad A_{1, i} C_{1, j} + A_{2, i} C_{2, j} = \text{Det} A \end{equation}
(3)	\begin{equation} i \neq j \quad \implies \quad A_{i, 1} C_{j, 1} + A_{i, 2} C_{j, 2} = 0 \end{equation}
(4)	\begin{equation} i \neq j \quad \implies \quad A_{1, i} C_{1, j} + A_{2, i} C_{2, j} = 0 \end{equation}