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

To determine the commutativity and associativity of the binary operation \( * \) defined on \( \mathbb{R} \) by the expression \( a * b = a - b + ab \), we will proceed step by step.

### Step 1: Check Commutativity

To check if the operation is commutative, we need to verify whether \( a * b = b * a \) for all \( a, b \in \mathbb{R} \).

1. **Calculate \( a * b \)**:
\[
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