n×n Matrix Determinant Calculator
Compute the determinant of any n×n square matrix using Gaussian elimination with partial pivoting, and check whether the matrix is invertible.
Last updated:
Input
Enter one matrix row per line, separating numbers with spaces or commas. The matrix must be square (same number of rows and columns).
Result
Determinant (det A)
8
Size
3×3
Invertible
Yes
Input matrix
| 2 | 1 | 0 |
| 1 | 3 | 1 |
| 0 | 1 | 2 |
How it works
- Enter the matrix with one row per line, separating the numbers in each row with spaces or commas. Only square n×n matrices (equal number of rows and columns) can be evaluated.
- The determinant is computed with Gaussian elimination using partial pivoting (equivalent to LU decomposition). The largest-magnitude entry is chosen as the pivot for numerical stability, the matrix is reduced to upper-triangular form, and the product of the diagonal entries is taken and signed according to the number of row swaps.
- A non-zero determinant means the matrix is invertible (non-singular) and has an inverse. A determinant of zero means the matrix is singular and has no inverse.
- Because of floating-point arithmetic the result may carry tiny rounding errors. Values smaller than about 1e-9 in magnitude are shown as 0.
Reviews
Tell us what you think of this calculator.
Write a review
Found an incorrect result or a problem? Turn this on to report it.
Rating