(a) Prove that the set is closed under multiplication.G = {z = a + bi ? C | a2 + b2 = 1}(Assume z = a+bi,w = c+di ? G. Compute zw = (?1)+(?2)i (expand and rearrange to find real and imaginary parts,) then prove (?1)2 + (?2)2 = 1.)(b) Find the simplified formula for z?1, the multiplicative inverse of z = a + bi ? G and verify z?1 ? G.Let G = {I, A, B, C} where the elements are matrices below. Prove that G is closed A .under multiplication by constructing a multiplication table..(e) (143)?S4 ?2 ?2?(f) ?3 4 ? M2(R) ?2 ?2?(g) ?3 4 ? GL2(R)

a) Prove that the set is closed under multiplication. G = {z = a + bic C | a2 + b2 = 1} Assume z = a+bi,w = c+di e G. Compute zw = (?1)+(?2)i (expand and earrange to find real and imaginary parts,) then prove (?1)2 + (?2)2 = 1.)