Then the product matrix \\(A \cdot B\\) consists of all possible dot products of a row from \\(A\\) with a column from \\(B\\):

\\[
A \cdot B
=
\begin{bmatrix}
\text{---} & a_1 & \text{---} \\\\
\text{---} & a_2 & \text{---} \\\\
& \vdots & \\\\
\text{---} & a_m & \text{---}
\end{bmatrix}
\cdot
\begin{bmatrix}
\vert & \vert & & \vert \\\\
b_1 & b_2 & ... & b_n \\\\
\vert & \vert & & \vert
\end{bmatrix}
=
\begin{bmatrix}
a_1 \cdot b_1 & a_1 \cdot b_2 & \text{---} & a_1 \cdot b_n \\\\
a_2 \cdot b_1 & a_2 \cdot b_2 & \text{---} & a_2 \cdot b_n \\\\
a_m \cdot b_1 & a_m \cdot b_2 & \text{---} & a_m \cdot b_n
\end{bmatrix}
\\]