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\$$.