8. Let S be the set of all 2 x 2 matrices of the form where x is an integer. Assume that S is a ring with respect to matrix addition and multiplication. (a) Is S a commutative ring? (b) Does S have a unity? (c) Does S have zero divisors?

8. Let S be the set of all 2 x 2 matrices of the form where x is an integer. Assume that S is a ring with respect to matrix addition and multiplication. (a) Is S a commutative ring? (b) Does S have a unity? (c) Does S have zero divisors?

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

8. Let S be the set of all 2 x 2 matrices of the form
where x is an integer. Assume that S is a
ring with respect to matrix addition and multiplication.
(a) Is S a commutative ring?
(b) Does S have a unity?
(c) Does S have zero divisors?

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