 Hi and welcome to the session. I am Shashi and I am going to help you to solve the following question. Question is show that none of the operations given above has identity. Sixth part of the previous question is A star B is equal to AB square where star is the binary operation on the 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 and element E 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. On set Q binary operation star is defined as A star B is equal to AB square. Now let E be the identity element in Q. Then A star E must be equal to A must be equal to E star A for every A belonging to Q where Q is the set of rational numbers. Now first of all let us find out A star E this is equal to A square which must be equal to A. Now we will find E star A E star A is equal to E A square which further must be equal to A by this equation but this is not possible. So we can write there is no element E in Q with A square is equal to E A square is equal to A for every A belonging to Q. So there exists no identity element for binary operation star. This completes the session. Hope you understood the session. Take care and goodbye.