Before we discuss solutions, we must appreciate the textbook itself. Most abstract algebra texts define a group on page one and never look back. Pinter does something different.
Critical Step: Notice we used associativity implicitly. Also, note that this proof works for any group, finite or infinite. Students try to "cancel" a and b from the middle without using the inverse multiplication carefully. Always multiply on the extreme left or right. a book of abstract algebra pinter solutions better