Definition:Classical Algorithm/Primitive Multiplication/Base 10 Multiplication Table

Definition
The primitive multiplication operation for conventional base $10$ arithmetic of two $1$-digit integers can be presented as a pair of operation tables as follows:


 * $\begin{array}{c|cccccccccc}

p & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 2 & 0 & 2 & 4 & 6 & 8 & 0 & 2 & 4 & 6 & 8 \\ 3 & 0 & 3 & 6 & 9 & 2 & 5 & 8 & 1 & 4 & 7 \\ 4 & 0 & 4 & 8 & 2 & 6 & 0 & 4 & 8 & 2 & 6 \\ 5 & 0 & 5 & 0 & 5 & 0 & 5 & 0 & 5 & 0 & 5 \\ 6 & 0 & 6 & 2 & 8 & 4 & 0 & 6 & 2 & 8 & 4  \\ 7 & 0 & 7 & 4 & 1 & 8 & 5 & 2 & 9 & 6 & 3  \\ 8 & 0 & 8 & 6 & 4 & 2 & 0 & 8 & 6 & 4 & 2  \\ 9 & 0 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1  \\ \end{array} \qquad \begin{array}{c|cccccccccc} c & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 \\ 3 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 2 & 2 & 2 \\ 4 & 0 & 0 & 0 & 1 & 1 & 2 & 2 & 2 & 3 & 3 \\ 5 & 0 & 0 & 1 & 1 & 2 & 2 & 3 & 3 & 4 & 4 \\ 6 & 0 & 0 & 1 & 1 & 2 & 3 & 3 & 4 & 4 & 5 \\ 7 & 0 & 0 & 1 & 2 & 2 & 3 & 4 & 4 & 5 & 6 \\ 8 & 0 & 0 & 1 & 2 & 3 & 4 & 4 & 5 & 6 & 7 \\ 9 & 0 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \end{array}$