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Determine whether or not the definiti...

Determine whether or not the definition of * On `R` , define by `a*b=a b^2` gives a binary operation. In the event that * is not a binary operation give justification of this. Here, `Z^+` denotes the set of all non-negative integers.

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On `R`, the binary operation `∗` defined by
`a∗b=ab^2`
Consider the values of `a=1` and `b=2` for the provided equation.
`1*2=1 ( 2 ) ^2 =4`
For the given case such that `a,binR` , the function provides the value that is defined in its range.
So it is deduced that the function `(*)` have a unique element `ab^ 2 inR` .
It means that the function `*` carries each pair `( a,b )` to a unique element `a*b=a b^ 2 in R` .
Thus, the function `*` is a binary operation.
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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