How the Matrix Calculator works.
det(A) uses elimination; (AB)ᵢⱼ = Σ AᵢₖBₖⱼMatrix A and Matrix B each have independently selected rectangular dimensions. Multiplication requires A columns to equal B rows; addition and subtraction require equal dimensions.
Worked example for the Matrix Calculator.
The determinant of [[1,2],[3,4]] is 1×4 − 2×3 = −2, so the matrix is nonsingular and invertible.
How to read this result.
The calculator returns a formatted matrix, determinant, or inverse and states when dimensions or singularity make the requested operation undefined.
How the calculation works
Matrix addition and subtraction combine matching cells; multiplication takes row-by-column dot products; determinants and inverses use elimination. Formula or rule: det(A) uses elimination; (AB)ᵢⱼ = Σ AᵢₖBₖⱼ. Matrix A and Matrix B each have independently selected rectangular dimensions. Multiplication requires A columns to equal B rows; addition and subtraction require equal dimensions.
What this calculator does not prove
Floating-point elimination can accumulate rounding error. The tool is limited to matrices up to 6×6 and is not a symbolic algebra or numerical linear-algebra certification system. Use the result for the mathematical question shown here; a correct calculation does not by itself establish that the source data, sample, or real-world assumption is appropriate.
Inputs and edge cases to check.
Matrices must be rectangular, contain finite numbers, have matching dimensions for addition/subtraction, and have compatible dimensions for multiplication.
What this tool does not include.
Floating-point elimination can accumulate rounding error. The tool is limited to matrices up to 6×6 and is not a symbolic algebra or numerical linear-algebra certification system.
Reference guidance and methodology.
Matrix Calculator questions.
What does the Matrix Calculator calculate?
Add, subtract, multiply, find determinants, or invert small matrices with dimension and singularity checks.
Which formula or algorithm does it use?
det(A) uses elimination; (AB)ᵢⱼ = Σ AᵢₖBₖⱼ. Matrix A and Matrix B each have independently selected rectangular dimensions. Multiplication requires A columns to equal B rows; addition and subtraction require equal dimensions.
What limitations or edge cases matter?
Matrices must be rectangular, contain finite numbers, have matching dimensions for addition/subtraction, and have compatible dimensions for multiplication. Floating-point elimination can accumulate rounding error. The tool is limited to matrices up to 6×6 and is not a symbolic algebra or numerical linear-algebra certification system.