15. Let 0: M2(Z) → Z where M₂(Z) is the ring of 2 × 2 matrices over the integers Z.Prove or disprove that each of the following mappings is a homomorphism.ba.o ([a= ad - bcb. 0• ([a b])= a + d (This mapping is called the trace of the matrix.)

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Answered: 15. Let 0: M2(Z) → Z where M₂(Z) is the…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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15. Let 0: M2(Z) → Z where M₂(Z) is the ring of 2 × 2 matrices over the integers Z. Prove or disprove that each of the following mappings is a homomorphism. b a. o ([a = ad - bc b. 0 • ([a b]) = a + d (This mapping is called the trace of the matrix.)