I have found this interesting Matrix Multiplication cases where multiplying two 2 x 2 Matrices concatenates the entries. Does this have a name ? Has this been found before ?
\begin{gather*} Some\ solutions\ to\ below\ eqn:\\ \\ \begin{pmatrix} a & b\\ c & d \end{pmatrix} \times \begin{pmatrix} e & f\\ g & h \end{pmatrix} =\begin{pmatrix} 10*a+e & 10*b+f\\ 10*c+g & 10*d+h \end{pmatrix}\\ \\ are\\ \\ \begin{pmatrix} 3 & 8\\ 3 & 8 \end{pmatrix} \times \begin{pmatrix} 3 & 8\\ 3 & 8 \end{pmatrix} =\begin{pmatrix} 33 & 88\\ 33 & 88 \end{pmatrix}\\ \\ \begin{pmatrix} 6 & 5\\ 9 & 8 \end{pmatrix} \times \begin{pmatrix} 3 & 5\\ 9 & 5 \end{pmatrix} =\begin{pmatrix} 63 & 55\\ 99 & 85 \end{pmatrix}\\ \\ \begin{pmatrix} 7 & 5\\ 8 & 6 \end{pmatrix} \times \begin{pmatrix} 5 & 5\\ 8 & 4 \end{pmatrix} =\begin{pmatrix} 75 & 55\\ 88 & 64 \end{pmatrix}\\ \\ \begin{pmatrix} 3 & 2\\ 7 & 3 \end{pmatrix} \times \begin{pmatrix} 8 & 2\\ 7 & 8 \end{pmatrix} =\begin{pmatrix} 38 & 22\\ 77 & 38 \end{pmatrix}\\ \\ \begin{pmatrix} 3 & 3\\ 6 & 5 \end{pmatrix} \times \begin{pmatrix} 6 & 3\\ 6 & 8 \end{pmatrix} =\begin{pmatrix} 36 & 33\\ 66 & 58 \end{pmatrix}\\ \\ \begin{pmatrix} 3 & 8\\ 4 & 7 \end{pmatrix} \times \begin{pmatrix} 7 & 4\\ 2 & 9 \end{pmatrix} =\begin{pmatrix} 37 & 84\\ 42 & 79 \end{pmatrix}\\ \\ \begin{pmatrix} 8 & 4\\ 6 & 3 \end{pmatrix} \times \begin{pmatrix} 8 & 4\\ 6 & 3 \end{pmatrix} =\begin{pmatrix} 88 & 44\\ 66 & 33 \end{pmatrix} \end{gather*}