Let G be the set consisting of the following matrices: (6 9) (6 ) ( ) -1/2 v3/2 V3/2 1/2 -1/2 V3/2) -1/2 -1/2 V3/2) -V3/2 1/: V3/2 -1/2 Show that G forms a group under multiplication, and write the Cay- ley table for this group.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.5: Normal Subgroups
Problem 2E: 2. Show that is a normal subgroup of the multiplicative group of invertible matrices in .
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Let G be the set consisting of the following matrices:
-1/2 v3/2
V3/2 1/2
( )()(器9).
-1/2
V3/2)
-1/2
1/2
V3/2)
-
-V3/2
1/:
V3/2 -1/2
Show that G forms a group under multiplication, and write the Cay-
ley table for this group.
Transcribed Image Text:Let G be the set consisting of the following matrices: -1/2 v3/2 V3/2 1/2 ( )()(器9). -1/2 V3/2) -1/2 1/2 V3/2) - -V3/2 1/: V3/2 -1/2 Show that G forms a group under multiplication, and write the Cay- ley table for this group.
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