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Let G = : a – b = c – d, a,b, c, d E R Show that G is a group under (the usual) matrix addition.

Let G = : a – b = c – d, a,b, c, d E R Show that G is a group under (the usual) matrix addition.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.1: Definition Of A Group
Problem 39E: 39. Let be the set of all matrices in that have the form for arbitrary real numbers , , and ....
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How do you prove G is a group given the definition provided

Group Let G be a set together with a binary operation ·, that assigns to (a, b) E G × G an element a · b in G (usually written as ab). We say (G, ·) is a group if it satisfies the following three properties: 1. Associativity; (ab)c= a(bc) for all a, b, c e G. 2. Identity; there exist an element e E G such that ae = a = ea for all a E G. The element e is called the identity element in G. 3. Inverses; for all a E G, there exist b E G such ab = e = ba. We denote b by a it the inverse of a. and call
Transcribed Image Text:Group Let G be a set together with a binary operation ·, that assigns to (a, b) E G × G an element a · b in G (usually written as ab). We say (G, ·) is a group if it satisfies the following three properties: 1. Associativity; (ab)c= a(bc) for all a, b, c e G. 2. Identity; there exist an element e E G such that ae = a = ea for all a E G. The element e is called the identity element in G. 3. Inverses; for all a E G, there exist b E G such ab = e = ba. We denote b by a it the inverse of a. and call
Let {(: ) G = : a – b = c – d, a,b, c, d E R Show that G is a group under (the usual) matrix addition.
Transcribed Image Text:Let {(: ) G = : a – b = c – d, a,b, c, d E R Show that G is a group under (the usual) matrix addition.
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