Discuss the commutativity and associativity of the binary operation * on R defined by `a`*`b=a-b+a b` for all `a , b in R ,` where on RHS we have usual addition, subtraction and multiplication of real numbers.

Explanation

Given * is a binary operation on R

defined by `a`*`b=a−b+ab`

Commutativity:

for any `a,binR`

We have `a`*`b=a−b+ab` and `b`*`a=b−a+ba`

Since, `a−b+ab ne b−a+ab`

`therefore a`*`b ne b`*`a`

So, * is not commutative on R

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