Inverse Matrix Calculator
A square matrix has an inverse only when its determinant is not zero; for a 2×2 matrix [[a, b], [c, d]] the inverse is 1/(ad − bc) · [[d, −b], [−c, a]].
At a glance
| What it is | Find the inverse of a 2×2, 3×3 or larger matrix online with exact fraction answers. Shows when a matrix has no inverse. Free, no sign-up. |
|---|---|
| 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 inverse | (1 ÷ (ad − bc)) · [[d, −b], [−c, a]] |
|---|---|
| Exists when | det(A) ≠ 0 |
| Check | A · A⁻¹ = I (identity matrix) |
| Example | [[4, 7], [2, 6]]⁻¹ = [[3/5, −7/10], [−1/5, 2/5]] |
| Larger matrices | Gauss–Jordan: row-reduce [A | I] to [I | A⁻¹] |
Why are the answers shown as fractions?
Inverses usually involve dividing by the determinant, so Plotline keeps exact fractions such as 3/5 instead of rounded decimals. That makes it easy to check homework answers.
How to use it in Plotline
- Matrix A is filled in with an example and A⁻¹ is calculated.
- Change the entries or the size; type A^-1 or inv(A) and press Enter.
- Tap a result matrix to save it as a new matrix and keep working with it.
Frequently asked questions
Why does my matrix have no inverse?
Because its determinant is 0, which makes the matrix singular. Its rows or columns are multiples of each other, so the transformation flattens space and cannot be undone. Only a square matrix with a non-zero determinant has an inverse.
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
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Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.