The set of residue classes modulo 5 is equipped with the usual operations of multiplication and addition of residue classes. If we denote -a for the additive inverse of element a with respect to addition, and a^-1 for the multiplicative inverse of element a with respect to multiplication, then the following holds: (a) 2^-1 + (-3) = 4 (b) (-4) * 4 = 4 (c) 3 + 3^-1 = 1 (d) (-1) * 1 = 0 (e) (-2) * 4^-1 = 3.
The set of residue classes modulo 5 is equipped with the usual operations of multiplication and addition of residue classes. If we denote -a for the additive inverse of element a with respect to addition, and a^-1 for the multiplicative inverse of element a with respect to multiplication, then the following holds: (a) 2^-1 + (-3) = 4 (b) (-4) * 4 = 4 (c) 3 + 3^-1 = 1 (d) (-1) * 1 = 0 (e) (-2) * 4^-1 = 3.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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The set of residue classes modulo 5 is equipped with the usual operations of multiplication and addition of residue classes. If we denote -a for the additive inverse of element a with respect to addition, and a^-1 for the multiplicative inverse of element a with respect to multiplication, then the following holds:
(a) 2^-1 + (-3) = 4
(b) (-4) * 4 = 4
(c) 3 + 3^-1 = 1
(d) (-1) * 1 = 0
(e) (-2) * 4^-1 = 3.
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