Determinant Calculator
The determinant of a 2×2 matrix [[a, b], [c, d]] is ad − bc; for example det([[4, 7], [2, 6]]) = 4·6 − 7·2 = 10. Enter any square matrix up to 10×10 below.
At a glance
| What it is | Free determinant calculator for 2×2, 3×3 and larger matrices up to 10×10, with exact fraction answers. Learn the ad − bc formula. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| 2×2 formula | det([[a, b], [c, d]]) = ad − bc |
|---|---|
| 3×3 and larger | Cofactor expansion or row reduction |
| det = 0 | The matrix is singular (no inverse) |
| Product rule | det(AB) = det(A)·det(B) |
| Transpose | det(Aᵀ) = det(A) |
What does the determinant mean?
Geometrically, the determinant is the factor by which the matrix scales area (2×2) or volume (3×3). A negative determinant means the orientation is flipped, and zero means space is flattened, which is why such a matrix cannot be inverted.
How to use it in Plotline
- Matrix A is already filled in with an example and det(A) is calculated.
- Edit the cells (fractions like 1/3 are fine) or change the size with the rows and cols steppers.
- Type det(A) and press Enter for any other matrix.
Frequently asked questions
How do I find the determinant of a 3×3 matrix?
Set matrix A to 3 rows and 3 columns, type the entries, then enter det(A). By hand, expand along the first row: a(ei − fh) − b(di − fg) + c(dh − eg).
Is it free?
Yes. The matrix calculator is free with no account and no sign-up, and there is no limit on how many matrices you work with. Determinants, inverses, RREF, multiplication and systems of equations are all included, and it works offline once loaded.
Learn more
Related
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Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.