Let `S` be the set of all real numbers except -1 and let * be an operation defined by `a*b=a+b+a b` for all `a ,\ b in Sdot` Determine whether * is a binary operation on `Sdot` If yes, check its commutativity and associativity. Also, solve the equation `(2*x)*3=7.`

Explanation

* be defined on `S`
by `a`*`b=a+b+a b`,
for all `a ,b in S`

Then we have to prove that

(i)* is a binary operation on S

Now take `a+b+ab+1=0`

`a+ ab + b+1 = 0`

`implies a(1+b)+1(1+b) = 0`

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