Consider the set S of ordered pairs of real numbers together with the operation defined by (a, b)* (c, d) = (ac - bd, ad + bc). a. Is the set an Abelian group? Justify. b. Solve for (5, 3)-¹, (-2, 9)-¹ and [(-2, 9) *(5, 3)]-¹.
Consider the set S of ordered pairs of real numbers together with the operation defined by (a, b)* (c, d) = (ac - bd, ad + bc). a. Is the set an Abelian group? Justify. b. Solve for (5, 3)-¹, (-2, 9)-¹ and [(-2, 9) *(5, 3)]-¹.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 23E: 23. Let be a group that has even order. Prove that there exists at least one element such that and...
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