Gaussian elimination / RREF
Exact fractions and a full row-operation trace.
Open calculatorMathematics / Free calculator
Matrix operations
Multiply, add, subtract, transpose, invert, or find the determinant and rank of a matrix.
01 Your inputs
02 Your result
Enter your values and select Calculate.
The method
A worked example
For A = [1 2; 3 4] and B = 2I, AB = [2 4; 6 8]. det(A) = −2 and A⁻¹ = [−2 1; 3/2 −1/2].
Assumptions & limits
Exact rational arithmetic; matrices up to 7×7. Products require matching inner dimensions; sums require identical shapes. Inverse and determinant require square matrices. Singular matrices have no inverse. Rational numerators and denominators must stay below 260 digits, and scientific notation exponents are limited to ±15.
Calculation source: Math Workbench: exact rational matrix arithmetic.