In each part following, a rule is given that determines a binary operation * on the set Z of all integers. Determine in each case whether the operation is commutative or associative and whether there is an identity element. Also find the inverse of each invertible element.

In each part following, a rule is given that determines a binary operation * on the set Z of all integers. Determine in each case whether the operation is commutative or associative and whether there is an identity element. Also find the inverse of each invertible element.

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter1: Introduction To Algebra

Section1.4: Translating Words Into Symbols

Problem 2MRE

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Question

In each part following, a rule is given that determines a binary operation * on the set
Z of all integers. Determine in each case whether the operation is commutative or
associative and whether there is an identity element. Also find the inverse of each
invertible element.

е. х*у — Зху
f. х * у — х — у
g. х*у — х + ху +у
h. x * y = x + y + 3

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