Number of binary operations on the set {a, b} are

A binary operation * on $\{a, b\}$ is a function from $\{a, b\} \times\{a, b\} \rightarrow\{a, b\}$

i.e., ${ }^{*}$ is a function from $\{(a, a),(a, b),(b, a),(b, b)\} \rightarrow\{a, b\}$.

Hence, the total number of binary operations on the set $\{a, b\}$ is $2^{4}$ i.e., 16 .

The correct answer is B.