Which of the following sets with an internal binary operation does not have an inverse for every element? (a) Z2\{0} with the usual multiplication of residue classes. (b) Z\{0} with the usual multiplication of integers. (c) {[1 a;0 1]∈R^2×2 ∣ a∈R} with the usual multiplication of matrices. (d) C\{0} with the usual multiplication of complex numbers. (e) S^1={z∈C ∣ ∣z∣=1} with the usual multiplication of complex numbers.

Which of the following sets with an internal binary operation does not have an inverse for every element? (a) Z2\{0} with the usual multiplication of residue classes. (b) Z\{0} with the usual multiplication of integers. (c) {[1 a;0 1]∈R^2×2 ∣ a∈R} with the usual multiplication of matrices. (d) C\{0} with the usual multiplication of complex numbers. (e) S^1={z∈C ∣ ∣z∣=1} with the usual multiplication of complex numbers.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

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Question

Which of the following sets with an internal binary operation does not have an inverse for every element?

(a) Z2\{0} with the usual multiplication of residue classes.

(b) Z\{0} with the usual multiplication of integers.

(d) C\{0} with the usual multiplication of complex numbers.

(e) S^1={z∈C ∣ ∣z∣=1} with the usual multiplication of complex numbers.

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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