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🧮 Matrix Determinant Calculator

Choose a matrix size, enter the entries row by row, and instantly get the determinant.

Matrix Size

Row 1, Col 1

Row 1, Col 2

Row 1, Col 3 (3×3 only)

Row 2, Col 1

Row 2, Col 2

Row 2, Col 3 (3×3 only)

Row 3, Col 1 (3×3 only)

Row 3, Col 2 (3×3 only)

Row 3, Col 3 (3×3 only)

What this calculator does

This tool calculates the determinant of a 2×2 or 3×3 square matrix, a single number that summarizes important properties of the matrix, such as whether it can be inverted.

The formulas used

For a 2×2 matrix with entries a, b (row 1) and c, d (row 2), the determinant is ad − bc. For a 3×3 matrix, this calculator uses cofactor expansion along the first row: det = a11(a22a33 − a23a32) − a12(a21a33 − a23a31) + a13(a21a32 − a22a31). This is the standard method taught in linear algebra courses.

Good to know

A determinant of zero means the matrix is "singular" and cannot be inverted — the calculator flags this for you. For a 2×2 matrix, leave the extra 3×3-only fields at their default values since they are not used in the calculation. Intended for general educational and reference use.

Last reviewed August 2026