Overview
Enter a square matrix (one row per line, values separated by commas) to calculate its determinant. Uses cofactor expansion along the first row, which is exact and straightforward to verify by hand for the sizes this tool supports (up to 4×4) - larger matrices are typically solved with LU decomposition instead for performance reasons, which isn't necessary at this scale. Useful for linear algebra coursework, checking whether a matrix is invertible (a zero determinant means it isn't), or verifying a calculation by hand. Runs entirely client-side.
Best for: Checking linear algebra homework or verifying whether a matrix is invertible
How to use this tool
- Enter your matrix. One row per line, values separated by commas - must be square (same number of rows and columns).
- Determinant is computed instantly. Calculated using cofactor expansion, exact for matrices up to 4×4.
- Read the result. A zero determinant means the matrix is singular (not invertible).
Frequently asked questions
A determinant of 0 means the matrix is singular - it has no inverse, and the linear system it represents either has no solution or infinitely many, rather than exactly one.
Cofactor expansion is simple and exact, but its cost grows factorially with matrix size, making it impractical beyond small matrices. Larger matrices are normally solved with LU decomposition instead - a different algorithm better suited to that scale, which this tool doesn't implement.