Matrix Determinant Calculator
2×2 and 3×3 determinants with cofactor working.
Enter your values
ⓘ Live results
Results
- Determinant
- 49
- Invertible?
- Yes
- Trace
- 7
- Volume scale factor
- 49
- Orientation
- Preserved
Working
- 12(0·5 − -1·4) − -3(2·5 − -1·1) + 1(2·4 − 0·1)
- 2= 49
Quick answer
A determinant measures how a matrix scales area or volume; a determinant of zero means the matrix is singular and has no inverse.
det = a(ei − fh) − b(di − fg) + c(dh − eg)
How to use the Matrix Determinant Calculator
- 1Pick 2×2 or 3×3.
- 2Type each row as comma-separated numbers.
- 3A non-zero determinant means the system has a unique solution.
Worked example
Using the values the calculator loads with:
Inputs
- Matrix size3 × 3
- Row 12, -3, 1
- Row 22, 0, -1
- Row 3 (3×3 only)1, 4, 5
Results
- Determinant49
- Invertible?Yes
- Trace7
- Volume scale factor49
- OrientationPreserved
- 2(0·5 − -1·4) − -3(2·5 − -1·1) + 1(2·4 − 0·1)
- = 49
Frequently asked questions
What does a determinant of zero mean?
The rows are linearly dependent: the matrix squashes space flat, so it cannot be inverted and the linear system has no unique solution.
Does row swapping change it?
Yes — each swap flips the sign, and multiplying a row by k multiplies the determinant by k.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.