ThmDex – An index of mathematical definitions, results, and conjectures.

Real arithmetic expression for the determinant of a 2-by-2 real square matrix

Formulation 0

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}

Then \begin{equation} \text{Det} A = a d - b c \end{equation}

Proofs

Proof 0

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}