 Hello and welcome to the session, again understand the following problem to take defining operation star on the set 0, 1, 2, 3, 4, 5 as A star B is equal to A plus B, if A plus B is less than 6 and A plus B minus 6, if A plus B is greater than equal to 6, show that the 0 is the identity for the operation and each element A of the set is invertible with 6 minus A being the inverse of A. Now, let us write the solution. The integral to our set is 0, 1, 2, 3, 4, 5, binary operation is defined as B is equal to A plus B, if A plus B is less than 6 and A plus B minus 6, if A plus B is greater than equal to 6, we have to show that 0 is the identity for the operation star, the element is equal to 0 star A which is equal to A. Now, 0 is equal to A plus 0 which is equal to A and 0 star A is equal to 0 plus A which is equal to A, star 0 is equal to 0 star A which is equal to A. Therefore, 0 is the identity element. Now, we have to show that each element of the set is invertible, A is the inverse of and A. Now, let us write the solution. We know B is the inverse of element A, star B is equal to B star A which is equal to 0, where 0 is the identity and A belongs to set 0, 1, 2, 3, 4, 5, minus A is equal to A plus 6 minus A which is equal to 0 and A which is equal to 6 minus A plus A minus 6 which is equal to 0. Each element 2, 3, 4, 5 is invertible, inverse is. I hope you understood this problem. Bye and have a nice day.