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Check whether the operation is commutative and associative
Given:
\( a * b = b \quad \forall a,b \in A \)
Commutativity:
\( a * b = b \)
\( b * a = a \)
Clearly:
\( a * b \neq b * a \quad (\text{when } a \neq b) \)
❌ Operation is NOT commutative
Associativity:
LHS:
\( (a*b)*c = b * c = c \)
RHS:
\( a*(b*c) = a * c = c \)
Thus:
\( (a*b)*c = a*(b*c) \)
✔ Operation is associative
Conclusion:
❌ Not commutative, ✔ Associative