Determinant, inverse, RREF, rank, product, transpose, and eigenvalues with every row operation animated as a step — in exact fractions.
Tip: use samples, upload, copy, download, and send-to actions inside the workspace where available.
Matrix Step Calculator is a free, browser-based tool that helps you get the job done quickly. Determinant, inverse, RREF, rank, product, transpose, and eigenvalues with every row operation animated as a step — in exact fractions. It's built for speed and privacy: Everything runs locally in your browser — your data is never uploaded to a server. No sign-up, no installs, and no daily limits.
Use this tool as the focused step in a larger browser-based workflow.
Review the preview, copy or download the result, and keep everything local in your browser.
Equation Step Solver: Solve linear equations, quadratics, and 2×2 systems with every step shown — discriminant, formula substitution, factored form, and a live graph of the roots.
Open toolSystem of Linear Equations: Solve linear systems with RREF, Gauss-Jacobi, and Gauss-Seidel methods using full step-by-step tables.
Open toolInterpolation Calculator: Step-by-step Newton forward/backward, divided difference & Lagrange interpolation with full tables.
Open toolCompute det(A) by cofactor expansion along the first row: det(A) = Σ a(1,j)·C(1,j), where C(1,j) = (−1)^(1+j)·det(M(1,j)) and the minor M(1,j) is A with row 1 and column j deleted.
| 2 | 1 | 1 |
| 1 | 3 | 2 |
| 1 | 0 | 0 |
Compute det(A) by cofactor expansion along the first row: det(A) = Σ a(1,j)·C(1,j), where C(1,j) = (−1)^(1+j)·det(M(1,j)) and the minor M(1,j) is A with row 1 and column j deleted.
| 2 | 1 | 1 |
| 1 | 3 | 2 |
| 1 | 0 | 0 |
Delete row 1 and column 1 (highlighted) to get the minor M(1,1); compute its 2×2 determinant, then apply the checkerboard sign (−1)^(1+1) = +1.
| 3 | 2 |
| 0 | 0 |
Delete row 1 and column 2 (highlighted) to get the minor M(1,2); compute its 2×2 determinant, then apply the checkerboard sign (−1)^(1+2) = −1.
| 1 | 2 |
| 1 | 0 |
Delete row 1 and column 3 (highlighted) to get the minor M(1,3); compute its 2×2 determinant, then apply the checkerboard sign (−1)^(1+3) = +1.
| 1 | 3 |
| 1 | 0 |
Multiply each entry of row 1 by its cofactor and add the three products.
| 2 | 1 | 1 |
| 1 | 3 | 2 |
| 1 | 0 | 0 |
