Understand the subject
How does a matrix equation solve?
For AX=B or XA=B, an inverse multiplies on the side that removes A.
Use it to keep multiplication order explicit while solving an eligible equation.
See the structure
What the calculation is doing
[ 1 1 | 3 ]R₂ − 2R₁[ 2 1 | 4 ]→pivots reveal the solution
Worked interpretation
Read the result in context
AX=B ⇒ X=A⁻¹B; XA=B ⇒ X=BA⁻¹
Interpret with care
Important boundary
Matrix multiplication does not commute, so solving on the wrong side changes the equation.
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
AX=B ⇒ X=A⁻¹B; XA=B ⇒ X=BA⁻¹
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
The coefficient matrix must be square and nonsingular.
AX=B ⇒ X=A⁻¹B; XA=B ⇒ X=BA⁻¹
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.
