 Hi and welcome to the session. My name is Shashi and I am going to help you to solve the following question. The question says, let me mean whether or not each of the definition of star given below gives a binary operation in the event that star is not a binary operation. Give justification for this. Third part is on R where R is the center for real numbers. Define star by A star B is equal to AB square. Let us now start the solution. We have given A star B is equal to AB square. Now we have to find if star is a binary operation on R where R is the set of real numbers. So we can write for every AB belonging to set of real numbers we get a unique value of AB square belonging to R where R is the set of real numbers. So we can write A star B is equal to AB square. This is given in the question and AB square belongs to set of real values. So this implies star is a binary operation and our required answer is yes. This completes the session. Hope you understood the session. Goodbye.