Matrix inverse calculator
Type the matrix one row per line to get its inverse A⁻¹, where A × A⁻¹ = I. If the determinant is zero, there is no inverse.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter matrix (one row per line).
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
A⁻¹ = adj(A) ÷ det(A), where adj(A) is the transpose of the cofactor matrix Cij = (-1)^(i+j) × det(Mij). For 2 × 2: [a b; c d]⁻¹ = [d -b; -c a] ÷ (ad - bc).
Example
Result: Inverse (exact fractions): 3/5 -7/10 -1/5 2/5; Determinant: 10.
4 7 2 6
3/5 -7/10 -1/5 2/5
Limits and caveats
- Accepts square matrices from 2 × 2 to 4 × 4.
- Exact fractions appear only when every entry is a whole number.
Questions about this tool
When does a matrix have an inverse?
When it is square and its determinant is not zero.
How can I check the inverse?
Multiply the matrix by its inverse; you should get the identity matrix I, with 1 on the diagonal and 0 elsewhere.
What is the inverse of [4 7; 2 6]?
The determinant is 4×6 - 7×2 = 10, so the inverse is [6 -7; -2 4] ÷ 10 = [0.6 -0.7; -0.2 0.4].