Matrix Calculator

Perform matrix operations including addition, multiplication, transpose, determinant, inverse, adjugate, rank, trace, eigenvalues, eigenvectors, LU decomposition, and linear system solving.
All processing happens locally in your browser — your data is never uploaded to any server.

Matrix A

Matrix B

Scalar k

Operations
Select an operation to compute the result.
Matrix Input: Click cells to edit values. Use Tab to move between cells. Change dimensions with the Rows/Cols controls.
Operations: A + B, A − B (same dimensions), A × B (compatible dimensions), scalar multiplication, transpose, determinant, inverse, adjugate, rank, trace, eigenvalues/eigenvectors, LU decomposition, and linear system solving Ax = b.
NOTE: Matrix B is used for A+B/A−B/A×B operations. For Ax = b, B is treated as a column vector b.
Matrices and determinants

A matrix is a rectangular grid of numbers; multiplying matrices composes the linear transformations they represent — and composition is order-dependent, which is why A×B ≠ B×A in general. The determinant det(A) summarizes a square matrix in one number: how much the transformation scales areas (2×2) or volumes (3×3).

det(A) = 0 means the transformation flattens space, so it cannot be undone — no inverse exists and Ax = b has no unique solution; that single number is why singular matrices matter.