Relation is Symmetric iff Inverse is Symmetric

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

Proof
Suppose $\mathcal R$ is symmetric.

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

The result follows.