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

On R, defined * by a*b = ab2


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

Given that ‘*’ is an operation that is valid in the Real Numbers ‘R’ and it is defined as given:


⇒ a*b = ab2, where a,b∈R


Since a∈R and b∈R,


According to the problem it is given that on applying the operation ‘*’ for two given real numbers it gives a real number as a result of the operation,


⇒ a*b∈R ...... (1)


We know that ab∈R if a∈R and b∈R


∴ The operation * defines a binary operation on R.


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