Multiplying matrices looks like it should work like ordinary multiplication — it doesn't, and that surprise is the point. Matrix multiplication composes transformations: rotate a 3D model and then scale it, and the product matrix does both at once, which is why every video game engine multiplies thousands of matrices per frame. The rule: the entry in row i, column j of the product is the dot product of row i of the first matrix with column j of the second. And there's a gatekeeper — the inner dimensions must match. A 2×3 matrix can multiply a 3×4 matrix (the 3s agree), producing a 2×4 result; a 2×3 times a 2×3 is simply illegal.

Order matters too: AB and BA are usually different matrices, sometimes dramatically so — rotate-then-scale is not scale-then-rotate, and graphics programmers who mix them up get sheared, inside-out models. This calculator multiplies your two matrices: enter the values as the First Number and Second Number inputs and read the Product. The essential check before trusting any matrix product is dimensional: write the shapes as (m×n)(n×p) = (m×p), confirm the inner pair matches, and the outer pair predicts your answer's shape.

With the pre-filled defaults — First Number 10, Second Number 5 — the Matrix Multiplication Calculator returns Product 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.