 Hi and welcome to the session. I am Shashi and I am going to help you to solve the following question is show that none of the operations even above has identity. The third part even in the previous question is A star B is equal to A plus AB where star is a binary operation on set Q of rational numbers. First of all let us understand the key idea to solve the given question. Given a binary operation star from A cross A to A an element A belonging to A if it exists is called identity of the operation star if A star E is equal to A is equal to E star A for every A belonging to set A. Let us now start with the solution. We know on set Q binary operation star is defined as A star B is equal to A plus AB right. Now let us assume A with an identity element in Q where Q is the set of rational numbers. A star E must be equal to A must be equal to E star A right for every A belonging to set Q. Now let us find out A star E we know A star E is equal to A plus A which must be equal to A. Now let us find out E star A we know E star A is equal to E plus EA which must be equal to A. We know A plus AE would not be equal to E plus EA so A star E is not equal to E star A so there does not exist any element E in Q plus AE equal to A plus EA for every A belonging to set Q. The final answer is there is identity element for binary operation star. This completes the session. Hope you understood the session. Take care and goodbye.