ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5519 on D5718: Real matrix determinant
Subresult of R5518: Complex arithmetic expression for the determinant of a 2-by-2 complex square matrix
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}