Let R^* be the set of all real numbers except 0. Define * on R^* by letting a * b = |a |^b.
a. Show that * gives an associative binary operation on R^*. 

b. Show that there is a left identity for * and a right inverse for each element in R^*. 

c. Is R^* with this binary operation a group? 

d. Explain the significance of this exercise.