11.1.1. Groups Homomorphisms 1. Which of the following maps are homomorphisms? If themap is a homomorphism, what is the kernel?+ ((ad)) = ₁CO: M₂ (R)→ R by ob,where M₂ (R) is the additive group of 2 × 2 matrices withentries in R.

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Answered: 1. Which of the following maps are…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 2E: 2. Show that is a normal subgroup of the multiplicative group of invertible matrices in .

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1. Which of the following maps are homomorphisms? If the map is a homomorphism, what is the kernel? = b, where M₂ (R) is the additive group of 2 x 2 matrices with entries in R. 4: M₂ (R) → R by ø ((ab) φ: C