 Hi and welcome to the session. I am Shashin and I am going to help you to solve the following question. The question is show that none of the operations given above has identity. Fourth part given in the previous question is A star B is equal to A minus B whole square 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 E belonging to set 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. Now let us start with the solution on set Q that is the set of rational numbers. Binary operation star is defined as A star B is equal to A minus B whole square. Now let us assume E with the identity element in set Q. A star E must be equal to A must be equal to E star A for every A belonging to set Q. Now let us find out A star E we know A star E is equal to A minus E whole square which must be equal to A by this equation but this can't be possible. A minus E whole square can never have the value equal to A. So we can write there is no element E in Q with A minus E whole square equal to A for every A belonging to Q. So our final answer is there is no identity element for binary operation star. This completes the session. Hope you understood the session. Take care and goodbye.