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2. a) The operation in a finite group can be specified by writing down a table. Write the table for (Z9,) and use it to show that (Z9,) is a group. Find the inverse of 2 and 5 in (Z9,0).

2. a) The operation in a finite group can be specified by writing down a table. Write the table for (Z9,) and use it to show that (Z9,) is a group. Find the inverse of 2 and 5 in (Z9,0).

Advanced Engineering Mathematics
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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2. a) The operation in a finite group can be specified by writing down a table. Write the table for (Z9,) and use it to show that (Z9,) is a group. Find the inverse of 2 and 5 in (Z.). b) Let G be the set of all 2x2 matrices [ b, a, b eR and a² + b² +0. Show that (G,*) where is the matrix multiplication forms a group. c) Let (G,+) be a group. Then (G,) is abelian if and only if (a - b)² = a² + b² for all a, b e G.
Transcribed Image Text:2. a) The operation in a finite group can be specified by writing down a table. Write the table for (Z9,) and use it to show that (Z9,) is a group. Find the inverse of 2 and 5 in (Z.). b) Let G be the set of all 2x2 matrices [ b, a, b eR and a² + b² +0. Show that (G,*) where is the matrix multiplication forms a group. c) Let (G,+) be a group. Then (G,) is abelian if and only if (a - b)² = a² + b² for all a, b e G.
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