How it works
Matrix multiplication takes the dot product of each row in the first matrix with each column in the second. The inner dimensions must match; this page provides a focused 2×2 tool.
Standard formula
Cᵢⱼ = Σ AᵢₖBₖⱼWorked example
[[1, 2], [3, 4]] × [[5, 6], [7, 8]] = [[19, 22], [43, 50]].
Frequently Asked Questions
Can I reverse the matrices?
Usually no. Matrix multiplication is not commutative, so AB can differ from BA.
How is each entry calculated?
Multiply matching row and column entries, then add the products.
Does this support larger matrices?
This focused version supports 2×2 matrices. Larger matrices can be added as a separate tool.
Can entries be negative or decimal?
Yes. All matrix entries accept finite numbers.