Notation for matrix permutation

Question

Say I have some matrices. $$\begin{bmatrix}0 & 1\\2 & 3\end{bmatrix} \begin{bmatrix}5 & 6\\7 & 8\end{bmatrix}$$ What notation would I use to show show that I am creating a matrix of every combination of their elements?

Answer 1

You could define a set $S$ of the elements/entries of the matrices: $S = \{0,1,2,3,5,6,7,8\}$. You could define these matrices as $[a_{ij}]$, where $a_{ij} \in S$ for $i,j=1,2$.