Question

The operation  is defined on the set R of real numbers by ab=ab+a.

Determine whether or not the operation  is associative.​

Please I need help.

Answer 1

ab=ab+a

We need to check the following:

(ab)c=a(bc) or not

LHS

(ab)c=(ab+a)c

=(ab+a)c+(ab+a)

=abc+ac+ab+a

RHS

a(bc)=a(bc+b)

=a(bc+b)+a

=abc+ab+a

as LHS ≠ RHS, the operation is not associative

Explanation: