Matrix determinant calculator
Enter a 2×2 or 3×3 matrix to get its determinant.
Matrix determinant calculator
Calculate the determinant of a 2×2 or 3×3 matrix. The determinant tells you whether a matrix is invertible (non-zero) and how it scales area or volume in a linear transformation.
Formulas
For a 2×2 matrix [[a, b], [c, d]], the determinant is ad − bc. For a 3×3 matrix it expands along the first row using 2×2 minors (the rule of Sarrus gives the same result). A determinant of 0 means the matrix is singular and has no inverse.
Frequently asked questions
What does a zero determinant mean? The matrix is singular — its rows (or columns) are linearly dependent and it can’t be inverted.
What is the determinant used for? Solving linear systems (Cramer’s rule), finding inverses, and measuring area/volume scaling.