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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Question 2. Let M(2, Q) be the set of all 2 × 2 matrices with entries from Q, i.e.,
{[a b]: a, b,c,d € Q}, where Q is the ring of rational numbers under the
M (2, Q) = {[a
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 [123
[2] in (M(2, Q), +)
3. Let M(2,Q)* be the set of all 2 × 2 matrices with entries from Q except []
Is M(2,Q)* a group under the usual matrix multiplication? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe00cebfb-aec4-474d-8979-79a2d105b819%2F71fbd3f0-b2a2-4e41-a1c1-2394b3a53576%2F7qzldii_processed.png&w=3840&q=75)
Transcribed Image Text:Question 2. Let M(2, Q) be the set of all 2 × 2 matrices with entries from Q, i.e.,
{[a b]: a, b,c,d € Q}, where Q is the ring of rational numbers under the
M (2, Q) = {[a
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 [123
[2] in (M(2, Q), +)
3. Let M(2,Q)* be the set of all 2 × 2 matrices with entries from Q except []
Is M(2,Q)* a group under the usual matrix multiplication? Justify your answer.
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