Discuss the commutativity and associativity of binary operation * defined on `Q` by the rule `a*b=a-b+a b` for all `a , b in Q`

Explanation

`a^{*} b=a-b+a b forall a, b in A=Q-{1}`
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b^{*} a=b-a+b a`
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(a^{*} b) neq b^{*} `a therefore * is not commutative.
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(a * b)^{*} c=(a-b+a b)^{*} c`
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=a-b-c+a b+a c-b c+a b c`
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a(b^{*} c)=a^{*}(b-c+b c) `
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=a-b+c+a b-a c-b c+a b c`
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(a^{*} b)^{*} c neq a^{*}(b^{*} c) `

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