Determinant Calculator

What is a Determinant?

The determinant is a scalar value that can be calculated from a square matrix. It provides critical information about the matrix, such as whether it is invertible (a matrix is invertible if and only if its determinant is non-zero).

For a 2 × 2 matrix, the determinant is calculated as ad - bc.

For a 3 × 3 matrix, we often use Laplace Expansion, where we multiply elements of a row by their corresponding cofactors. Geometrically, the absolute value of the determinant represents the area (2D) or volume (3D) scaling factor of the linear transformation described by the matrix.