Add, multiply, invert and analyse matrices up to 8 × 8.
Each entry of A × B is a row of A times a column of B. [[1,2],[3,4]] × [[5,6],[7,8]] = [19, 22] [43, 50].
Enter one or two matrices (one row per line, numbers separated by spaces or commas) and choose an operation: A + B, A − B, A × B, k × A, transpose, determinant, inverse, rank or trace. The result is shown as a table, with the determinant and trace of the result for square matrices. The size rules are checked for you with clear messages.
Matrix multiplication needs the columns of A to equal the rows of B; the inverse exists only for square matrices with a non-zero determinant. Related tools: the Quadratic Formula Calculator, Scientific Calculator and Statistics Calculator.
The calculator applies the standard method step by step.
| Col 1 | Col 2 | |
|---|---|---|
| Row 1 | 19 | 22 |
| Row 2 | 43 | 50 |
| Property | Value |
|---|---|
| Determinant | 4 |
| Trace | 69 |
| Operation | Result |
|---|---|
| A × B | 2 × 2 matrix |
| A + B | 2 × 2 matrix |
| Determinant of A | -2 |
| Inverse of A | 2 × 2 matrix |
| Transpose of A | 2 × 2 matrix |
Multiply each row of the first by each column of the second and add the products. The columns of A must equal the rows of B.
A single number computed from a square matrix; if it is 0 the matrix is singular and has no inverse.
Use Gauss-Jordan elimination; the inverse exists only if the matrix is square and its determinant is not zero.
Swapping rows and columns, so entry (i, j) moves to (j, i).
The number of linearly independent rows (or columns).
The sum of the diagonal entries of a square matrix.
It uses the standard method: (AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ A × A⁻¹ = I det by elimination The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
