Matrix Determinant Calculator
Calculate the determinant of a square matrix of any size.
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Enter a square matrix to calculate its determinant.
Rows separated by semicolons, entries by commas — e.g. "1,2;3,4" for a 2x2 matrix. Must be square.
Your result
-2
Determinant
AI explanation
Formula
Computed via Gaussian elimination with partial pivoting for numerical stabilityWorked example
Determinant of [[1,2],[3,4]]
| Field | Value |
|---|---|
| Matrix | 1,2;3,4 |
| Determinant | -2 |
Assumptions
- Only a square matrix has a determinant — a non-square matrix shows an error.
Frequently asked questions
What does a matrix's determinant tell you?
Among other things, whether the matrix is invertible (a zero determinant means it's singular, with no inverse) and how it scales area/volume when used as a linear transformation.
How is the determinant calculated for a large matrix?
Via Gaussian elimination — reducing the matrix to upper-triangular form (tracking row swaps for sign) and multiplying the diagonal entries, which is far more efficient than cofactor expansion for larger matrices.
What does a determinant of 0 mean?
The matrix is "singular" — it has no inverse, and its rows/columns are linearly dependent.