Matrix - Determinant

The determinant of a matrix is a special number that can be calculated from its elements. The determinant is only defined for square matrices.

Computing

For a 2 x 2 matrix:

$$A=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$$

the determinant, denoted as det(A) or |A|, is calculated as:

$$\text{det}(A)=ad-bc$$

For higher-dimensional square matrices, the determinant can be computed using various methods, such as expansion by minors, row reduction, or using properties of determinants.