Matrices for reflexive, symmetric and antisymmetric relations
A matrix for the relation R on a set A will be a square matrix.
R is reflexive iff all the diagonal elements (a11, a22, a33, a44) are 1.
R is symmetric iff any two elements of it that are symmetric with
respect to the NE-SW diagonal are both 0 or both 1.
R is antisymmetric iff no two distinct elements of it that are symmetric
with respect to the NE-SW diagonal are both 0 or both 1.