(a) Show that the set of matrices given above equipped with the operation of matrix multiplication is a group. (b) Show that this group is not abelian.

Elementary Linear Algebra (MindTap Course List)
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Chapter3: Determinants
Section3.CM: Cumulative Review
Problem 17CM: Find the sequence of the elementary matrices whose product is the non singular matrix below. [2410]
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(a) Show that the set of matrices given above equipped with the operation of matrix multiplication is a group. (b) Show that this group is not abelian.
Consider the set that consists of the following six matrices
0
1
-- () -- () --(-9)
I
=
A
=
B =
1
1
-1
-1
-1
-1
10
c = ( ₁ ) ² = ( ₁ ) × =(:; 9)
с
D=
K
1
1
-1
-1
-
Transcribed Image Text:Consider the set that consists of the following six matrices 0 1 -- () -- () --(-9) I = A = B = 1 1 -1 -1 -1 -1 10 c = ( ₁ ) ² = ( ₁ ) × =(:; 9) с D= K 1 1 -1 -1 -
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