Answered: Let R be a ring with unity. Assume…

Let R be a ring with unity. Assume b1a=1R and ab2=1R. Prove that b1=b2. Also, let R be a ring with unity. Assume a and b are both units. Prove that (ab)-1=b-1a-1.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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Let R be a ring with unity. Assume b₁a=1_Rand ab₂=1_R. Prove that b₁=b_2.

Also, let R be a ring with unity. Assume a and b are both units. Prove that (ab)^-1=b^-1a^-1.

Expert Solution

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Ring with unity,so 1_R is different from 0_R ,

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