Matrix Inverse Calculator
Invert a square matrix with Gauss-Jordan elimination.
How the matrix inverse calculator works
A matrix inverse reverses a linear transformation: multiplying the original matrix by its inverse gives the identity matrix. This calculator augments the input with an identity matrix, uses partial pivoting, normalizes each pivot row, and eliminates the pivot column from every other row. The transformed identity side is the inverse when all pivots exist.
For the default matrix with rows 1, 2 and 3, 4, Gauss-Jordan elimination returns rows minus 2, 1 and 1.5, minus 0.5. This is the verified inverse. Multiplying it by the original produces identity entries one on the diagonal and zero elsewhere, apart from possible floating-point rounding.
Reading matrix inverse calculator results privately
The matrix must be square and nonsingular. If a pivot cannot be found above the tolerance, the page reports that no inverse exists instead of dividing by an unstable value. Decimal matrices are supported, but near-singular inputs can magnify rounding dramatically. Exact fractional output, symbolic entries, and generalized pseudoinverses are not included. This matrix inverse calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
How can I check an inverse?
Multiply the original matrix by the reported inverse. The product should be the identity matrix within ordinary rounding tolerance.
Why does a singular matrix have no inverse?
A singular matrix maps different inputs to the same output, so no transformation can uniquely reverse it.
Is the matrix inverse calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
Browse the full set of free, private, in-browser tools.