a) Let R be a ring with identity and let a,b ∈ R be invertible. Prove that ab is also invertible.
a) Let R be a ring with identity and let a,b ∈ R be invertible. Prove that ab is also invertible.
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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a) Let R be a ring with identity and let a,b ∈ R be invertible. Prove that ab is also invertible.
b) Prove that the set of invertible elements R^× forms a group.
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