Consider the subset 1 a a b S = 0 1 1 c : a, b, c € Z3 } C SL3(Z3). 0 0 1 (a) Show that S is a subgroup of SL3(Z3). (b) Show that every non-trivial element of S has order 3. (c) Is S abelian? Justify your answer.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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2. Consider the subset
{(
1 а b
0 1
0 0 1
S =
: a, b, c € Z3 } C SL3(Z3).
(a) Show that S is a subgroup of SL3(Z3).
(b) Show that every non-trivial element of S has order 3.
(c) Is S abelian? Justify your answer.
Transcribed Image Text:2. Consider the subset {( 1 а b 0 1 0 0 1 S = : a, b, c € Z3 } C SL3(Z3). (a) Show that S is a subgroup of SL3(Z3). (b) Show that every non-trivial element of S has order 3. (c) Is S abelian? Justify your answer.
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