Relations and Zero One Matrices
The resulting zero-one representation is the $|A|\times |A|$ matrix $M$ with $M_{ij} = 1$ if $(i,j) \in R$, and $M_{ij} = 0$ if $(i,j) \notin R$. In our case, the matrix is
$$ M = \begin{pmatrix} 1 &amp; 1 &amp; 0 \\ 0 &amp; 0 &amp; 1 \\ 1 &amp; 0 &amp; 0 \end{pmatrix}. $$
Take it as an exercise to prove the following properties:


$R$ is reflexive iff the diagonal of $M$ is all 1s.
$R$ is symmetric iff $M$ is symmetric.
$R$ is antisymmetric iff the off-diagonal entries of $M+M^T$ are 0/1 (but not 2).
$R$ is transitive iff the support of $M^2$ is a subset of the support of $M$, where the support is the set of non-zero entries.