10. let h = ((0), (12)(34)) in a a. show that h is not normal in a b. referring to the multiplication table for a, in table 5.1 on page 111, show that, although

10. Let H = ((0), (12)(34)) in A a. Show that H is not normal in A b. Referring to the multiplication table for A, in Table 5.1 on page 111, show that, although a,H = a,H and a,H = a,,H, it is not true that a,H = a,a,,H. Explain why this proves that the left cosets ofH do not form a group under coset multiplication.