How to use it
Choose an operation, set the number of rows and columns for Matrix A (and Matrix B if the operation needs two), and type the entries. The result is shown straight away. You can add and subtract matrices of the same size; multiply A × B when the number of columns of A equals the number of rows of B; and find the determinant, the inverse, the trace and powers of square matrices. The transpose swaps rows and columns, and “k × A” multiplies every entry by a number. If an operation is not possible, such as multiplying matrices of the wrong shapes or inverting a singular matrix, the page explains why instead of showing a wrong answer.
What the operations mean
Each entry of a product A × B is the sum of a row of A multiplied term by term with a column of B, so the order matters: A × B is usually different from B × A. The determinant of a square matrix is a single number that tells you, among other things, whether it can be inverted: if it is 0, the matrix is singular and has no inverse. The inverse A⁻¹ is the matrix that gives the identity (ones on the diagonal, zeros elsewhere) when multiplied by A. The trace is the sum of the diagonal entries. Results are rounded to six decimal places for display.
Questions
What is the biggest matrix? 5 × 5. Can I enter fractions? Use decimals; fractions like 1/3 are not read. For fraction arithmetic, use the Fraction Calculator. Is my data sent anywhere? No, everything is worked out in your browser. What about solving equations? For a single quadratic equation, see the Quadratic Equation Solver.