Let $Q$ be a finite quiver and let $\mu_{k}$ denote mutation at a vertex $k$. Why is this an involution? I don't see it clear (should be easy though..)

What mutation? Of a cluster in the algebra, of a tilting module, of... ?
– Mariano Suárez-Alvarez♦Feb 19 '13 at 4:57

@Mariano Suárez-Alvarez: the mutation at a vertex of a finite quiver without loops or 2-cycles
– user31561Feb 19 '13 at 5:18

That is in fact an incarnation of cluster mutation. Have you played with Prof. Keller's famous JavaApplet (math.jussieu.fr/~keller/quivermutation), perhaps you will be able to see why this is the case after palying with the program for a while. Also, you should have stated where you have learnt this, be precise about what you are talking about. And if you think this is an easy question, it may be more appropriate to try asking this on StackExchange before just throwing a one line question on here and expecet everyone understands what you are talking about.
– Aaron ChanFeb 19 '13 at 16:27