Summary: Math 3130, Abstract Algebra
Homework 3 Key
4.1 Prove that in a group that
Remember: the group may not be commutative.
Solution: Directly check:
(a b) (b-1
) = (a (b b-1
= (a e) a-1
= a a-1
and so we have directly verified the inverse is as stated.
4.5 Recall that if z = x + iy is a complex number then the modulus of z is
|z| = x2 + y2
Prove that the complex numbers of modulus 1 form a group under multiplication.