Question

Let a,b be any two elements of a group. Prove that' (ab)-1 = b-1a-1

Let a,b be any two elements of a group. Prove that'

(ab)-1 = b-1a-1

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
let g be a group. let h be a subgroup of g. define a~b. if ab^-1...
let g be a group. let h be a subgroup of g. define a~b. if ab^-1 is in h. prove ~ is an equivalence relation on g
2. Let a and b be elements of a group, G, whose identity element is denoted...
2. Let a and b be elements of a group, G, whose identity element is denoted by e. Prove that ab and ba have the same order. Show all steps of proof.
(abstract alg) Let G be a cyclic group with more than two elements: a) Prove that...
(abstract alg) Let G be a cyclic group with more than two elements: a) Prove that G has at least two different generators. b) If G is finite, prove that G has an even number of generators
A) Prove that a group G is abelian iff (ab)^2=a^2b^2 fir any two ekemwnts a abd...
A) Prove that a group G is abelian iff (ab)^2=a^2b^2 fir any two ekemwnts a abd b in G. B) Provide an example of a finite abelian group. C) Provide an example of an infinite non-abelian group.
1. Let a and b be elements of a group, G, whose identity element is denoted...
1. Let a and b be elements of a group, G, whose identity element is denoted by e. Assume that a has order 7 and that a^(3)*b = b*a^(3). Prove that a*b = b*a. Show all steps of proof.
Let G be a group. Prove that following statements are equivalent. a.) G is commutative b.)...
Let G be a group. Prove that following statements are equivalent. a.) G is commutative b.) ∀ a,b ∈ G, (ab)2 = a2b2 c.) ∀ n ∈ N, ∀ a,b ∈ G, (ab)n = anbn
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0...
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0 (mod n), then a ≡ 0 (mod n) or b ≡ 0 (mod n). (b) Prove or disprove: Suppose p is a positive prime. If ab ≡ 0 (mod p), then a ≡ 0 (mod p) or b ≡ 0 (mod p).
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a,...
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a, c) = 1 and gcd(b, c) = 1. (Hint: use the GCD characterization theorem.) (b) Prove if gcd(a, c) = 1 and gcd(b, c) = 1, then gcd(ab, c) = 1. (Hint: you can use the GCD characterization theorem again but you may need to multiply equations.) (c) You have now proved that “gcd(a, c) = 1 and gcd(b, c) = 1 if and...
Let O ∈ (AB) and C /∈ AB. Prove that there is a point D on...
Let O ∈ (AB) and C /∈ AB. Prove that there is a point D on the same side of AB as C such that m(∠DOA) = m(∠COB).
How many electrons are needed for elements below to complete thier octet? a. group 1A elements...
How many electrons are needed for elements below to complete thier octet? a. group 1A elements b. group 6A elements c. group 5A elements d.group 2A elements
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT