Let \(\times\) be a binary operation on set of rational number \(\displaystyle\mathbb{Q}\) defined as follows: \(a\cdot b=a+b+2ab\), where \(\displaystyle{a},{b}\in\mathbb{Q}\)

a) Prove that \(\times\) is commutative, associate algebraic operation on \(\displaystyle\mathbb{Q}\)