  Given a skew left brace $\mathfrak{B}$, we introduce the notion of an
"opposite" skew left brace $\mathfrak{B}'$, which is closely related to the
concept of the opposite of a group, and provide several applications. Skew left
braces are closely linked with both solutions to the Yang-Baxter Equation and
Hopf-Galois structures on Galois field extensions. We show that the
set-theoretic solution to the YBE given by $\mathfrak{B}'$ is the inverse to
the solution given by $\mathfrak{B}$; this allows us to identify the group-like
elements in the Hopf algebra providing the Hopf-Galois structure using only
these solutions. We also show how left ideals of $\mathfrak{B}'$ correspond to
the realizable intermediate fields of a certain Hopf-Galois extension of a
Galois extension.
