Using the Matrix Calculator
Addition requires both matrices to have the same dimensions. Multiplication requires the number of columns in A to equal the number of rows in B. The output then has A’s row count and B’s column count.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- Matrix A (rows on separate lines)
- 1, 2 3, 4
- Matrix B (rows on separate lines)
- 5, 6 7, 8
- Operation
- Add
Example result
- Matrix
- 6 8 10 12
Method and assumptions
Addition is element-wise. Multiplication takes row–column dot products.
Check the answer in the original problem
After solving, substitute the result into the original equation or relationship where possible. This can catch a sign error or a coefficient entered in the wrong position. Keep the exact inputs available when comparing with another tool, since changing a coefficient or rounding an intermediate value can change the problem being solved.
Common question
Why does A × B differ from B × A?
The row–column combinations change when the order changes. Matrix multiplication is generally not commutative, even when both products are defined.
Guide updated .