Determinant Calculator

Enter the elements of a square matrix. Separate elements in a row with spaces or commas, and start each new row on a new line.

About the Determinant

  • A matrix has an inverse if and only if its determinant is non-zero.
  • The absolute value of the determinant represents the scaling factor of area (in 2D) or volume (in 3D) under the transformation.
  • A determinant of zero means the matrix maps the space into a lower dimension (e.g., a plane onto a line or point).

Common methods for calculation include cofactor expansion (used here for matrices larger than 2x2) and row reduction.