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 computes determinants, inverses, RREF, rank, products, transposes and eigenvalues while showing each row operation as its own step, in exact fractions rather than decimals. Exact arithmetic is the point: Gauss-Jordan elimination done in floating point hides small errors and produces answers like 0.9999999, which is precisely the confusion the tool is built to avoid.
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 |
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 |
