Matrix Multiplication Calculator

Multiply two matrices and see every dot product spelled out, in exact fractions - updating live as you type.

Matrix A dimension

Matrix B dimension

Matrix A

Matrix B

Your input

Multiply $[\begin{matrix} 1 & 2 & 3 \\ 1 & 2 & 3 \end{matrix}]$ by $[\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$ .

Solution

$C_{11} = 1 ∙ 1 + 2 ∙ 2 + 3 ∙ 3 = 14$

[\begin{matrix} 14 \\ □ \end{matrix}]

$C_{21} = 1 ∙ 1 + 2 ∙ 2 + 3 ∙ 3 = 14$

[\begin{matrix} 14 \\ 14 \end{matrix}]

Answer

The product matrix is $[\begin{matrix} 14 \\ 14 \end{matrix}]$ .

Runs entirely on your device - nothing is ever uploaded.

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How to use the matrix multiplication calculator

Set the dimensions - A's columns and B's rows are linked, so the pair is always multipliable.
Type a number (decimals and fractions like 1/5 both work) into every cell of both grids.
The solution writes itself: each element C_ij appears as its dot product - row i of A dotted into column j of B - with the running product matrix alongside.
Read the final product in exact fractions, or copy it.

No calculate button - solutions are always on, updating the moment you type.

Why order matters

Matrix multiplication is not commutative: AB rarely equals BA, and the shapes must line up - columns of A against rows of B. That order-sensitivity is the whole point in graphics, where rotate-then-move differs from move-then-rotate, and in neural networks, where each layer is a matrix multiply in a fixed sequence. Dimension mismatch is the classic error; this calculator flags it before any arithmetic.