Abstract matrix multiplication

Let \(\mathcal{V}=\mathbf{Bool}\). Here is matrix multiplication \(M*N\) with \(X=\bar{3}, Y=\bar{2},Z=\bar{3},M=X\times Y\rightarrow Z, N=Y\times Z\rightarrow B\).

\(X\)

\(Y\)

\(X*Y\) ?