Matrix Calculator
Add, subtract, multiply 2x2 or 3x3 matrices, or find a determinant.
| Enter values and click Calculate |
Matrix Operations
Matrix addition and subtraction work element by element - both matrices must be the same size, and you simply add or subtract the numbers in matching positions. Matrix multiplication is different: each entry in the result comes from multiplying a row of A by a column of B and summing the products, which is why matrix multiplication is not the same as multiplying elements directly.
The Determinant
The determinant is a single number calculated from a square matrix that reveals key properties - for instance, a matrix only has an inverse if its determinant is not zero. For a 2×2 matrix it is ad − bc; for a 3×3 matrix it's found by expanding along the first row using the same 2×2 pattern for each smaller sub-matrix.