Matrix Inverse Calculator
Calculate matrix inverse instantly in your browser.
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What this tool does
Calculate matrix inverse instantly in your browser. If the determinant is zero the matrix has no inverse — its rows are linearly dependent.
How to use the Matrix Inverse Calculator
- Enter or select matrix — rows separated by ; or new lines, entries by commas.
- Read the calculated result; change any measurement to compare alternatives.
Formula
The inverse A⁻¹ satisfies A × A⁻¹ = I (the identity matrix). It is found by Gauss–Jordan elimination: augment A with I and row-reduce until the left side becomes I, leaving A⁻¹ on the right.
- matrix
- Matrix — rows separated by ; or new lines, entries by commas
If the determinant is zero the matrix has no inverse — its rows are linearly dependent.
Worked example
For matrix inverse calculator, the following measurements illustrate the exact method: Matrix — rows separated by ; or new lines, entries by commas: 4, 7; 2, 6.
Inputs
- Matrix — rows separated by ; or new lines, entries by commas4, 7; 2, 6
Result
- Inverse matrix0.6, -0.7 ; -0.2, 0.4
- Determinant10
- Check: A × A⁻¹1, 0 ; 0, 1
Results explained
- Inverse matrix
- Inverse matrix from the formula above. If the determinant is zero the matrix has no inverse — its rows are linearly dependent.
- Determinant
- Determinant from the formula above. If the determinant is zero the matrix has no inverse — its rows are linearly dependent.
- Check: A × A⁻¹
- Check: A × A⁻¹ from the formula above. If the determinant is zero the matrix has no inverse — its rows are linearly dependent.
Frequently asked questions
The inverse A⁻¹ satisfies A × A⁻¹ = I (the identity matrix). It is found by Gauss–Jordan elimination: augment A with I and row-reduce until the left side becomes I, leaving A⁻¹ on the right.
If the determinant is zero the matrix has no inverse — its rows are linearly dependent.
Where mathematically meaningful, yes. Fields specify permitted ranges and undefined operations display an error.
Exact integer calculations use safe integers; decimal calculations use browser floating point, so small rounding differences can occur.
All values remain in your browser and are never uploaded.