So we have row vectors
\\(a_1 = \begin{bmatrix} 1 & 2 \end{bmatrix}\\),
\\(a_2 = \begin{bmatrix} 3 & 4 \end{bmatrix}\\),
\\(a_3 = \begin{bmatrix} 5 & 6 \end{bmatrix}\\),

and column vectors
\\(b_1 = \begin{bmatrix} 10 \\\\ 50 \end{bmatrix} \\),
\\(b_2 = \begin{bmatrix} 20 \\\\ 60 \end{bmatrix} \\),
\\(b_3 = \begin{bmatrix} 30 \\\\ 70 \end{bmatrix} \\),
\\(b_4 = \begin{bmatrix} 30 \\\\ 80 \end{bmatrix} \\).

So the product matrix \\(A \cdot B\\) is the 3-by-4 matrix of dot products \\(a_i \cdot b_j\\).