Question 2. Let M (2, Q) be the set of all 2 × 2 matrices with entries from Q, i.e., M(2, Q) = {[a b] : a, b, c, d € Q}, where Q is the ring of rational numbers under the usual addition and multiplication. 1. Show that (M(2, Q), +) is a group, where + is the usual matrix addition. 2. What is the inverse of [¹] in (M(2,Q), +) L3 2 3. Let M(2,Q)* be the set of all 2 × 2 matrices with entries from Q except 81. Is M(2,Q)* a group under the usual matrix multiplication? Justify your answer.

Question 2. Let M (2, Q) be the set of all 2 × 2 matrices with entries from Q, i.e., M(2, Q) = {[a b] : a, b, c, d € Q}, where Q is the ring of rational numbers under the usual addition and multiplication. 1. Show that (M(2, Q), +) is a group, where + is the usual matrix addition. 2. What is the inverse of [¹] in (M(2,Q), +) L3 2 3. Let M(2,Q)* be the set of all 2 × 2 matrices with entries from Q except 81. Is M(2,Q)* a group under the usual matrix multiplication? Justify your answer.

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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