Determinant of a Matrix

A determinant is a value that is useful in the analysis and solutions of systems of linear equations.

The determinant of the 2 × 2 square matrix

is the value of the expression ad – bc.

This number is useful in finding the inverse of the matrix, and in deciding whether the related system of equations

ax + by = 0

cx + dy = 0

has a solution (it does unless the determinant is equal to 0).

The determinant of the 3 × 3 matrix