Skill: Calculate the determinant of a 2 by 2 matrix

For a $2\times2$ matrix $\begin{pmatrix}a&b\\c&d\end{pmatrix}$, its determinant is $ad-bc$, so the products are subtracted in a specific order rather than added or treated as interchangeable. The determinant gives the signed area-scaling factor of the associated linear transformation; a zero determinant indicates dependent rows or columns and a noninvertible matrix, a fact useful in solving linear systems. Determinants of larger matrices and more abstract generalizations are not included.