Hi i need help with the following question

Let X={1,2,3,4} and let A be the set $\displaystyle X$ x $\displaystyle X$. Define a relation on A by

(x,y)R(w,z)<=>x+y=w+z

Show that R is an equivalence relation on A and describe (as subsets of A) the equivalence classes of R.

The first bit involving that the statement is a equivalence relation, i manged to do the following however i am not sure if it is correct though.

transitive since (x,y)R(x,y)=x+y=x+y

symmetric since (w,z)R(x,y)=w+z=x+y

transitive since (x,y)R(w,z) and let (w,z)R(u,v) ==> (x,y)R(u,v)=x+y=u+v

However i have no idea on how to do the equivalence class stuff.

thanks