Relation is Symmetric iff Inverse is Symmetric

Theorem
A relation $\mathcal R$ is symmetric its inverse $\mathcal R^{-1}$ is also symmetric.

Proof
Let $\mathcal R$ be symmetric.

Then from Relation equals Inverse iff Symmetric:
 * $\mathcal R = \mathcal R^{-1}$

The result follows.