Q: Find the matrix representing the relations S o R, where the matrices representing R and S. I am having difficulty understanding the following:
Find the matrix representing the relations $S\circ R$, where the matrices representing $R$ and $S$:
$$M_R = \begin{bmatrix}1 \ 0 \ 1 \\ 1 \ 1 \ 0 \\ 0 \ 0 \ 0\end{bmatrix} \text{ and }M_C = \begin{bmatrix}0 \ 1 \ 0 \\ 0 \ 0 \ 1 \\ 1 \ 0 \ 1\end{bmatrix} \implies M_R \odot M_S \implies \begin{bmatrix}1 \ 1 \ 1 \\ 0 \ 1 \ 1 \\ 0 \ 0 \ 0\end{bmatrix}$$
I know that if the composite matrix has $t_{ij} = 1$ if and only if $r_{ik} = s_{kj} = 1$ for some $k$. I am unsure how to arrive at the answer to the right.

A: Using standard matrix multiplication,
$$\pmatrix{1&0&1\\1&1&0\\0&0&0}\pmatrix{0&1&0\\0&0&1\\1&0&1}=\pmatrix{1&1&1\\0&1&1\\0&0&0}.$$
