Basic binary operation on set Hey please help me answer this question:
Given a set $A$ with at least 2 elements which on it the binary operation * is defined in that manner:
for every $a,b\in A,  a*b=b$.
Check if the binary operation * is commutative, associative and idempotent.

Say $A$ has at least two different elements, name them $5$ and $2$. Then $$5*2 = 2\ne 5 = 2*5$$
so it is not commutative.
Since we have also:
$$a*(b*c) = a*c = c$$ and $$(a*b)*c = b*c=c$$
we see it is associative. Also we have $b*b = b$ so ...
