Let M(2; R) denote the set of (2 x 2)-matrices with coefficients in the commutative ring R {0}, that is, a b -[] c d Then M (2; R) is a ring with respect to addition and multiplication of matrices. Show that M(2; R) has zero divisors and provide an example where M(2; R) is not commutative. M(2; R) = { | a, b, c, d = R}
Let M(2; R) denote the set of (2 x 2)-matrices with coefficients in the commutative ring R {0}, that is, a b -[] c d Then M (2; R) is a ring with respect to addition and multiplication of matrices. Show that M(2; R) has zero divisors and provide an example where M(2; R) is not commutative. M(2; R) = { | a, b, c, d = R}
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
![Let M(2; R) denote the set of (2 x 2)-matrices with coefficients in the commutative
ring R {0}, that is,
[ ]
M(2; R) := {
| a, b, c, d = R}
Then M (2; R) is a ring with respect to addition and multiplication of matrices.
Show that M(2; R) has zero divisors and provide an example where M(2; R) is not
commutative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F741f6be6-8829-482d-8847-4d6abe7c76ed%2F59895444-cd04-44a4-bfc3-4e0a0630a49e%2Fg0m9i8e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let M(2; R) denote the set of (2 x 2)-matrices with coefficients in the commutative
ring R {0}, that is,
[ ]
M(2; R) := {
| a, b, c, d = R}
Then M (2; R) is a ring with respect to addition and multiplication of matrices.
Show that M(2; R) has zero divisors and provide an example where M(2; R) is not
commutative.
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