Matrix Multiplication Calculator
Choose the size and enter the rows of matrix A and matrix B.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Entry (i, j) of A × B = row i of A · column j of B
- The product of two 2×2 or two 3×3 matrices has the same size
- The determinant of the product equals det(A) × det(B)
For one matrix on its own, see the matrix inverse calculator.
Worked example
[[1, 2], [3, 4]] × [[5, 6], [7, 8]]:
- Row 1: 1 × 5 + 2 × 7 = 19 and 1 × 6 + 2 × 8 = 22
- Product = [[19, 22], [43, 50]]
Why your number may differ
Values are rounded to 6 decimal places. For matrices of different shapes you need a general matrix tool.
Frequently asked questions
How do I multiply two matrices?
Each entry of the product is the dot product of a row of A with a column of B: multiply matching entries and add them up.
Does the order matter?
Yes. A × B is usually different from B × A.
What is the identity matrix?
The matrix with 1s on the diagonal and 0s elsewhere. Multiplying by it leaves a matrix unchanged.