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.