Matrix Calculator
Work with rational entries in matrices up to eight rows and columns. Choose addition, multiplication, determinant, inverse, reduced row echelon form or a unique square-system solution. Row-operation notes and a tab-separated export keep the result inspectable.
Your result
How the calculation works
Addition is element-wise. (AB)ij=Σ AikBkj. Gauss–Jordan elimination normalizes pivots and eliminates their columns to produce RREF. An inverse reduces [A|I] to [I|A⁻¹]; a system reduces [A|b].
Worked example
For A=[[1,2],[3,4]], determinant is −2 and inverse is [[−2,1],[3/2,−1/2]]. With b=[5,6], the unique solution is [−4,9/2].
Assumptions and limitations
Rows must have equal widths. Solve requires square A and one-column B. Singular inverses and nonunique systems are rejected. Exact arithmetic is bounded to 1,000-digit intermediate numerators and denominators.
Separate rows with new lines or semicolons and entries with spaces or commas. Use 1/3 for exact fractions; decimal entries are also parsed exactly.
Sources and editorial responsibility
Maintained by Renvoro Pty Ltd. Sources inform the methods and assumptions shown here; outputs have the limitations described on this page.
Method reviewed 2026-10-13. Calculation standards · Report an issue