Matrix Determinant Calculator
The matrix determinant calculator is your fast and easy way to get the determinant of any square matrix of size 2×2, 3×3, or 4×4.
Determinant-306
Size3×3
Invertible?Yesa non-zero determinant
Rank3
Trace11
Geometric meaning306the volume scale factor
Your matrix
| 6 | 1 | 1 |
| 4 | -2 | 5 |
| 2 | 8 | 7 |
The method
expand by cofactors, or reduce and multiply the pivots
What the determinant tells you
It is the factor by which the matrix scales area (2×2) or volume (3×3). A determinant of zero means the transformation collapses space into a lower dimension — which is exactly why such a matrix has no inverse: the collapse cannot be undone.
A negative determinant means the orientation is flipped as well as scaled.