Quaternion Conjugation is Involution

Theorem
Let $\mathbf x = a\mathbf 1 + b\mathbf i + c\mathbf j + d\mathbf k$ be a quaternion.

Let $\overline{\mathbf x}$ denote the quaternion conjugate of $\mathbf x$.

Then the operation of quaternion conjugation is an involution:


 * $\overline{\left({\overline{\mathbf x} }\right)} = \mathbf x$