Question

Determine whether or not the definition of * given below gives a binary operation. In the event that * is not a binary operation give justification of this.

On R, define by a*b = ab²

Here, Z⁺ denotes the set of all non-negative integers.

Answer 1

\[\ a, b \in R\] 
\[ \Rightarrow a, b^2 \in R\] 
\[ \Rightarrow a b^2 \in R\] 
\[ \Rightarrow a * b \in R\] 
\[\text{Thus}, *\text{ is a binary operation on R }.\]