Matrix Calculator

Adds and multiplies matrices A and B up to 6×6, finds the determinant, inverse, transpose, rank, reduced row echelon form (RREF) and eigenvalues, and solves AX = B. Use it to check linear algebra homework or to find an inverse that is long to do by hand.

How to use

1. Set "Rows" and "Columns" for "Matrix A" and "Matrix B" and type the values, or paste a table from a spreadsheet into a cell.
2. Press an operation button such as "A × B", "det X", "X⁻¹" or "AX = B". For operations on one matrix, choose A or B under "Matrix to use".
3. Under "Show results as", choose "Fractions (exact)" or "Decimals".
4. To keep calculating with the result, press "Send to A" or "Send to B". Use "Copy LaTeX" or "Copy (tab-separated)" to copy it.

How it works

• Cells accept whole numbers, decimals, fractions such as 1/3 and mixed numbers such as 1 1/2; empty cells count as 0. All arithmetic is done exactly with fractions.
• A × B needs as many columns in A as rows in B. Determinant, inverse, power and trace need a square matrix. If the sizes do not fit, the page says why.
• Eigenvalues are calculated for symmetric matrices and for matrices up to 3×3. Values that are not rational are shown to 10 significant digits.
• Your matrices are saved in this browser on this device.

Questions and answers

How do I find the inverse of a 2×2 matrix?

The inverse of [[a, b], [c, d]] is 1/(ad − bc) × [[d, −b], [−c, a]]. If ad − bc is 0, there is no inverse.

Why does it say the matrix has no inverse?

The matrix is singular: its determinant is 0. This happens when one row is a linear combination of the other rows.

Is matrix multiplication commutative?

No. In general A × B and B × A are different; press "A × B" and "B × A" to compare.

Can I solve a system of linear equations with it?

Yes. Put the coefficients in A and the constants in one column of B, then press "AX = B". The page tells you if there is no solution or infinitely many.