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Let R be a ring with identity, and let x e R be an element with a multiplicative inverse. Then the equation (-x) -(x¹) = 1 is true in R. Fill in the white boxes to make a proof of this fact. For each step in the proof, fill in the grey box to indicate which ring axiom or other fact is used to derive that step. Proof: . By ● By . By . By . By we have we have , we have we have we have (-x) -(x¹) = 1.

Let R be a ring with identity, and let x e R be an element with a multiplicative inverse. Then the equation (-x) -(x¹) = 1 is true in R. Fill in the white boxes to make a proof of this fact. For each step in the proof, fill in the grey box to indicate which ring axiom or other fact is used to derive that step. Proof: . By ● By . By . By . By we have we have , we have we have we have (-x) -(x¹) = 1.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let R be a ring with identity, and let xe R be an element with a multiplicative inverse. Then the equation (-x) =(x¹) = 1 is true in R. Fill in the white boxes to make a proof of this fact. For each step in the proof, fill in the grey box to indicate which ring axiom or other fact is used to derive that step. Proof: . By By ● By . By . By ● the additive inverse law You should fill all the boxes, so if you came up with a proof that doesn't fill them all, try including more intermediate steps. Please feel free to look up what question 4 from the week 6 tutorial says. uniqueness of additive inverses the multiplicative inverse law the multiplicative commutative law -(-1) = 1 we have we have we have we have we have (-x) -(x¹) = 1. -(-(x-x¹)) = 1 -(x -(x¹)) = 1 3 the distributive law 1+-1=0 (-x) - (-x)-¹ = 1 Question 4 from week 6 tutorial the multiplicative identity law (-1)-¹ = -1
Transcribed Image Text:Let R be a ring with identity, and let xe R be an element with a multiplicative inverse. Then the equation (-x) =(x¹) = 1 is true in R. Fill in the white boxes to make a proof of this fact. For each step in the proof, fill in the grey box to indicate which ring axiom or other fact is used to derive that step. Proof: . By By ● By . By . By ● the additive inverse law You should fill all the boxes, so if you came up with a proof that doesn't fill them all, try including more intermediate steps. Please feel free to look up what question 4 from the week 6 tutorial says. uniqueness of additive inverses the multiplicative inverse law the multiplicative commutative law -(-1) = 1 we have we have we have we have we have (-x) -(x¹) = 1. -(-(x-x¹)) = 1 -(x -(x¹)) = 1 3 the distributive law 1+-1=0 (-x) - (-x)-¹ = 1 Question 4 from week 6 tutorial the multiplicative identity law (-1)-¹ = -1
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