Basic binary operation on set

Question

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.

Answer 1

An answer emphasizing substitutions

Answer 2

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 ...