Q. 11 Let and ∗ be the binary operation on A defined by
Show that ∗ is commutative and associative. Find the identity element for ∗ on
A, if any.
and ∗ be the binary operation on A defined by
Thus it is commutative.
Thus, it is associative.
Let will be a element for operation * if for all .
This is not possible for any element in A .
Hence, it does not have any identity.