Inverse Matrices Calculator
Matrix Inverse Calculator works out Inverse and Inverse matrix from Matrix, Method and Decimals shown. The default figures on this page give inverse of 0.6 -0.7; -0.2 0.4; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
13 steps
- Matrix is 2x2.
- [ 4 7 ]
- [ 2 6 ]
- det(A) = 10
- Cofactor matrix C, where C(i,j) = (-1)^(i+j) det(minor(i,j)):
- [ 6 -2 ]
- [ -7 4 ]
- adj(A) = Cᵀ:
- [ 6 -7 ]
- [ -2 4 ]
- A⁻¹ = adj(A) / det(A) = adj(A) / 10:
- [ 0.6 -0.7 ]
- [ -0.2 0.4 ]
Inverse matrixtable
| 0 | 1 |
|---|---|
| 0.6 | -0.7 |
| -0.2 | 0.4 |
Its 4 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the Matrix Inverse Calculator calculates
Inverts a square matrix by the adjugate formula or Gauss-Jordan elimination, reporting the determinant, the cofactor and adjugate matrices, and singularity.
How to use this Matrix Inverse Calculator
Enter Matrix, Method and Decimals shown. Inverse updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Inverse, Inverse matrix and Determinant.
The method follows Gilbert Strang, Introduction to Linear Algebra, ch. 2.5 (inverse matrices) and ch. 5.3 (Cramer's rule, adjugate) and Wikipedia, Invertible matrix - methods of matrix inversion.
2x2 inverse example
With Matrix: 4 7; 2 6, the calculator returns Determinant: 10, Inverse: 0.6 -0.7; -0.2 0.4. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Inverse, Inverse matrix and Determinant. The inputs you can vary are Matrix, Method and Decimals shown.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
Can we do matrix inverse in a calculator?
Inverts a square matrix by the adjugate formula or Gauss-Jordan elimination, reporting the determinant, the cofactor and adjugate matrices, and singularity. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give 0.6 -0.7; -0.2 0.4.
How do I calculate the inverse of a matrix?
Inverts a square matrix by the adjugate formula or Gauss-Jordan elimination, reporting the determinant, the cofactor and adjugate matrices, and singularity. Open “How this is worked out” beside the result to see each step for your own figures.
How to do inverse matrix on TI-84 calculator?
It needs Matrix, Method and Decimals shown. Nothing else is required, and the figures stay in your browser.
How to find the inverse of 2x2 and 3x3 matrix?
The result gives Inverse, Inverse matrix, Determinant, Invertible, Order (n) and Rank, each labelled with its unit so the figure can be read on its own.
What information do I need for the Matrix Inverse Calculator?
You need Matrix, Method and Decimals shown. The page opens with default figures that give inverse of 0.6 -0.7; -0.2 0.4, so you can see the scale before entering your own.
What does this Matrix Inverse Calculator show?
It shows Inverse, Inverse matrix, Determinant, Invertible, Order (n), Rank, Adjugate matrix and Cofactor matrix, with the working and any warnings for your entries.