(Associativity check by putting the two light's associativity test tables on top of each other)
All elements in a cayley table:
Def 1: Given a magma $(M,\circ)$ of $n$ elements. Let $S$ be a $1 \times n$ matrix or $n \times 1$ matrix where its entries are elements $a \in M$. The cayley table is then given by the outer product $T=S \otimes S$, which is a $n \times n$ matrix. For all matrices, the tranpose is defined in the usual way, thus $(T^\textrm{T})^\textrm{T}=T$
Rows and columns
Def 2: Rows and columns of the cayley table are given in the usual way: For all $i\in M$, $T_{ai}$ is the…
