 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. The second part given above is A star B is equal to A square plus B square. Where star is the binary operation on set Q of rational numbers. First of all let us understand the key idea to solve the given question. We know 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. Another operation star is defined as A star B is equal to A square plus A square. Let us assume E with the identity element in Q. A star E must be equal to A must be equal to E star A right. Now let us find out A star E you know A star E is equal to A square plus E square which must be further equal to A but this can't be possible for every A belonging to Q. So we can write there exists no element E in Q with A square plus E square is equal to A for every A belonging to Q where Q is the set of all rational numbers. 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.