Inverse of Symmetric Relation is Symmetric

Theorem
Let $\mathcal R$ be a relation on a set $S$.

If $\mathcal R$ is symmetric, then so is $\mathcal R^{-1}$.

Proof
Let $\mathcal R$ be symmetric.

Then from Relation equals Inverse iff Symmetric it follows that $\mathcal R^{-1}$ is also symmetric.