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Question 2. Let M(4,Z) denote the set of all 4-by-4 matrices with integral entries. Together with matrix addition + and matrix multiplication, answer each of the following questions. Provide clear reasons for your answers. (a) Show that the pair (M(4,Z), +) is an additive group. Is it Abelian or not? 1 (b) Is the pair (M(4,Z),-) a group? (c) Does the triple M(4,Z), +, constitute a ring? (d) If it is a ring, is the ring commutative or not?

Question 2. Let M(4,Z) denote the set of all 4-by-4 matrices with integral entries. Together with matrix addition + and matrix multiplication, answer each of the following questions. Provide clear reasons for your answers. (a) Show that the pair (M(4,Z), +) is an additive group. Is it Abelian or not? 1 (b) Is the pair (M(4,Z),-) a group? (c) Does the triple M(4,Z), +, constitute a ring? (d) If it is a ring, is the ring commutative or not?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.4: Cyclic Groups
Problem 5E: The elements of the multiplicative group G of 33 permutation matrices are given in Exercise 35 of...
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Question 2. Let M(4,Z) denote the set of all 4-by-4 matrices with integral entries. Together with matrix addition + and matrix multiplication, answer each of the following questions. Provide clear reasons for your answers. (a) Show that the pair (M(4,Z), +) is an additive group. Is it Abelian or not? 1 (b) Is the pair (M(4,Z),-) a group? (c) Does the triple M(4,Z), +, constitute a ring? . (d) If it is a ring, is the ring commutative or not?
Transcribed Image Text:Question 2. Let M(4,Z) denote the set of all 4-by-4 matrices with integral entries. Together with matrix addition + and matrix multiplication, answer each of the following questions. Provide clear reasons for your answers. (a) Show that the pair (M(4,Z), +) is an additive group. Is it Abelian or not? 1 (b) Is the pair (M(4,Z),-) a group? (c) Does the triple M(4,Z), +, constitute a ring? . (d) If it is a ring, is the ring commutative or not?
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