If $A = \{a, b, c\}$,then the number of binary operations on $A$ is

Let $*$ be a binary operation defined on $Q$. Determine whether the binary operation defined by $a * b = a - b$ for all $a, b \in Q$ is commutative.

Show that $+: R \times R \rightarrow R$ and $\times: R \times R \rightarrow R$ are commutative binary operations,but $-: R \times R \rightarrow R$ and $\div: R_* \times R_* \rightarrow R_*$ are not commutative.

Let $*$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a * b = a^{2} + b^{2}$ for all $a, b \in Q$ is commutative.

Let $^*$ be the binary operation on $N$ given by $a \,^* \,b = \text{L.C.M. of } a \text{ and } b$. Find $5 \,^* \,7$ and $20 \,^* \,16$.

On the set of all natural numbers $N$,which one of the following $*$ is a binary operation?