Reverse operation on Quaternions

Question

I'm currently studying Clifford algebras and I came across a concept called reverse. It has the following properties:

1. $(AB)^† = B^†A^†$ for all $A$ and $B$.
2. $v^† = v$ for all vectors $v$.

I was wondering whether there was something similar in the Quaternions. By vectors I mean pure imaginary quaternions here. I know that conjugation $q^† = q^*$ fulfills the first rule but not the second one. Similarly $q^† = -q^*$ fulfills the second rule, but not the first one. Is there any involution that would fulfill both?