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Determinant (2×2)

The determinant of a square matrix is a single number that tells us a lot about the matrix, including whether it has an inverse. For a 2×2 matrix it is computed directly from the entries.

det⁡(abcd)=ad−bc\det\begin{pmatrix}a&b\\c&d\end{pmatrix} = ad-bc2×2 determinant

Symbols

det⁡A\det Athe determinant of A

Example

det⁡(2134)=2⋅4−1⋅3=5\det\begin{pmatrix}2&1\\3&4\end{pmatrix} = 2\cdot4-1\cdot3 = 5.

det⁡A=0\det A=0 means AA is not invertible, and that the columns are linearly dependent.
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Part of Linear Algebra and Differential Equations: Matrices.