c+CalcLantern

2×2 matrix inverse

Invert a nonsingular two-by-two matrix.

How this works

Inverse = [d, −b; −c, a]/(ad−bc).

Example

Using the example inputs, inverse matrix is [-2, 1; 1.5, -0.5].

Matrix, row-major
1, 2, 3, 4
Inverse matrix
[-2, 1; 1.5, -0.5]

Scope and assumptions

Nearly singular matrices may suffer amplified rounding error.

OpenStax mathematics

Related calculators

3×3 determinant

2×2 matrix multiplication

Vector dot product

Vector cross product

Percentage

BUILT FOR CLARITY

Useful tools. Honest answers.

An original collection of calculators for everyday estimates and learning.

Calculations run in your browser. This site does not send your inputs to a server or serve advertising. Optional analytics runs only after you allow it. Results are estimates within each tool’s stated scope, not professional advice.

Financial, health and building-related tools have specific limitations. Check important decisions with a qualified professional. No live currency rates, tax tables or current price feeds are connected.