Matrix Determinant Calculator
2×2 and 3×3 determinants with cofactor working.
Enter your values
Choose one of: 2 × 2, 3 × 3.
Enter the row 1 you are working with.
Enter the row 2 you are working with.
Enter the row 3 (3×3 only) you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | 2×2 and 3×3 determinants with cofactor working. |
|---|---|
| Category | Math |
| Inputs needed | Matrix size, Row 1, Row 2, Row 3 (3×3 only) |
| Main output | Determinant |
| Formula | det = a(ei − fh) − b(di − fg) + c(dh − eg) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Matrix size
- Choose one of: 2 × 2, 3 × 3.
- Row 1
- Enter the row 1 you are working with.
- Row 2
- Enter the row 2 you are working with.
- Row 3 (3×3 only)
- Enter the row 3 (3×3 only) you are working with.
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.
What do I need to enter into the Matrix Determinant Calculator?
Just 4 values: matrix size, row 1, row 2, row 3 (3×3 only). Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Matrix Determinant Calculator work out the answer?
A determinant measures how a matrix scales area or volume; a determinant of zero means the matrix is singular and has no inverse. It applies the formula det = a(ei − fh) − b(di − fg) + c(dh − eg) and shows the working so you can check each step by hand.
Is the Matrix Determinant Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.