Understand the subject
What is an inverse matrix?
An inverse undoes a square transformation: applying A and then A⁻¹ returns every vector to its original position.
Use it to reverse an invertible transformation or solve eligible matrix equations.
See the structure
What the calculation is doing
input vector× Aoutput vectorAA⁻¹=A⁻¹A=I
Worked interpretation
Read the result in context
AA⁻¹=A⁻¹A=I
Interpret with care
Important boundary
Only nonsingular square matrices have inverses.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Set the matrix dimensions required by the task.
- Fill every visible entry and any operation-specific control.
- Read the result type, factors, classification, and disclosed limitations.
Calculation method
Apply the stated linear-algebra contract
AA⁻¹ = A⁻¹A = I
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
The inverse exists exactly when det(A) is nonzero.
AA⁻¹ = A⁻¹A = I
Supported inputs
Precision and limits
Matrix size
Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.
Entry precision
Enter signed finite decimals with at most 30 digits and 15 decimal places.
Exactness
Finite decimals become reduced rational numbers and intermediate structural calculations are not rounded.
