det, inv, rank, eigen -- step by step

Matrix Calculator

Enter the entries of matrix A (and B, if the operation needs two matrices), pick an operation, and the calculator shows the result along with the row-reduction or cofactor-expansion steps behind it.

Matrix A

rows 3

cols 3

Matrix B

rows 3

cols 3

💡 You can paste a whole block of cells straight from Excel or Google Sheets — click a cell, paste, and the grid resizes to fit.

Apply to

Properties

Transformations

Decompositions

Arithmetic

How the results are checked

Exact, not rounded. Every operation runs through SymPy, a symbolic algebra engine, so a determinant comes back as a fraction or a radical rather than a decimal approximation.
The real working, not just an answer. For the determinant, inverse, row echelon form, rank, trace and eigenvalues, the steps reconstruct what was actually done: which rows were swapped, which pivot was used, which cofactor terms were summed.
Assumptions are flagged. If a matrix has a symbolic parameter and a pivot has to be assumed nonzero to continue, the steps mark it as an "Assumption" and a note says the result holds for generic values of the parameter.

Like any software, the calculator can contain bugs. For exams, publications or other important work, verify the result independently.

About the Service

This Matrix Calculator computes determinants, inverses, eigenvalues, eigenvectors, and several matrix decompositions (LU, QR, Cholesky), and shows the actual steps behind each result rather than just the final answer. Cells accept plain numbers, fractions, decimals, complex entries, or symbolic parameters like x or a_1, so the same tool works for a quick numeric check and for a linear algebra problem that needs an exact symbolic answer.

Matrix Calculator Features

Core operations: determinant, inverse, transpose, rank, trace, adjugate, row echelon form
Eigenvalues and eigenvectors, with a basis shown for each eigenspace
Decompositions: LU, QR, Cholesky, and the Moore–Penrose pseudoinverse
Matrix arithmetic: addition, subtraction, multiplication, scalar multiplication, integer powers
Matrices up to 8×8, with support for fractions, decimals, complex numbers, and symbolic entries
Paste a block of cells straight from Excel or Google Sheets — the grid resizes to fit
On-screen math keyboard for entering square roots, fractions, and functions on mobile
Light and dark themes

How It Works

Every operation runs through SymPy, a symbolic algebra engine, so results are exact rather than rounded — a determinant comes back as a fraction or a radical, not a decimal approximation. For determinant, inverse, row echelon form, rank, trace, and eigenvalues, the calculator reconstructs the actual working: which row got swapped, which pivot was used, which cofactor term contributed to the final sum. If a matrix contains a symbolic parameter, the calculator marks the point where it has to assume a pivot is nonzero to keep going, and notes that the result holds for generic values of that parameter rather than every possible one. QR and Cholesky decompositions are computed directly instead of narrated step by step, since writing out Gram–Schmidt orthogonalization by hand stops being readable even for small matrices.

How to Use the Calculator

Set the size of matrix A (and B, if your operation needs two matrices) using the row/column controls, then fill in the cells — or switch to text mode and type or paste the matrix as plain rows of numbers. Use the A/B toggle to choose which matrix a single-matrix operation applies to, pick an operation from the Properties, Transformations, Decompositions, or Arithmetic groups, and the result appears below with the worked steps. A+B, A−B, and A×B use both matrices automatically.