# NFA for right left multiplication

Given the following multiplication table how could one construct an NFA such that it accepts all strings that have a certain product (say a) ?

The string "abcb" would be evaluated as (a(b(cb))) = a

\begin{array}{c|ccc} \times & a & b & c \\ \hline a & a & a & c \\ b & c & a & b \\ c & b & c &a \end{array}

I tried to take the transpose of the above matrix:

\begin{array}{c|ccc} \times & a & b & c \\ \hline a & a & c & b \\ b & a & a & c \\ c & c & b & a \end{array}

And build an NFA for that. I then reversed all the transitions, but I don't think that works.