Binary operation Inverse?

Question

okay i totaly forgot how to find the inverse of "r"

* | p r s v
------------------
p | s v p r
r | v p r s
s | p r s v
v | r s v p

Answer 1

First you must find the identity element by inspecting the table.
Then you must find what, combined with"r", gives you this identity element.
By inspecting the table, it appears that s is the identity element. This is becuase each element, p r s v combined with s yields itself.
Next inspect the table and see what combined with r gives s.
That would be v.
Also note that v*r = r*v = s