Inverse Relation Properties

Theorem
If a relation $$\mathcal{R}$$ has any of the properties:


 * Reflexive
 * Antireflexive
 * Non-reflexive
 * Symmetric
 * Asymmetric
 * Antisymmetric
 * Non-symmetric
 * Transitive
 * Antitransitive
 * Non-transitive

... then $$\mathcal{R}^{-1}$$ has the same properties.