(1) a. On a set (A, B. C. of three distinct elements, a binary operation . is defined. The operation . is commutative and associative and it is given that A . B = A and B . C = Buse the associative property to prove that A . C = A. if A denotes - A and if other powers are similarly defined show that d' = A' . B. Hence or otherwise show that () A' cannot be C (1i) A' = B = B' = B If the operation table * has the following entries ABC Fill in the remaining entries and complete the table in the only possible way