2. Consider the set ·={+6 1] · *£ J*[ ]+[3]}, where the entries of these matrices are in Z3. The operation is matrix multiplication. (a) Prove that G is a group. (You can use the fact that matrix multiplication is associative.) (b) Is G commutative or non-commutative? (c) Recall that the order of an element g is the smallest positive exponent k such that where e is the identity element in the group. Find the order of each element in G. Any conjectures?
2. Consider the set ·={+6 1] · *£ J*[ ]+[3]}, where the entries of these matrices are in Z3. The operation is matrix multiplication. (a) Prove that G is a group. (You can use the fact that matrix multiplication is associative.) (b) Is G commutative or non-commutative? (c) Recall that the order of an element g is the smallest positive exponent k such that where e is the identity element in the group. Find the order of each element in G. Any conjectures?
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![2. Consider the set
G = { [ D] + [J] ¹ + 1] +[3]},
where the entries of these matrices are in Z3. The operation is matrix multiplication.
(a) Prove that G is a group. (You can use the fact that matrix multiplication is associative.)
(b) Is G commutative or non-commutative?
(c) Recall that the order of an element g is the smallest positive exponent & such that
where e is the identity element in the group. Find the order of each element in G. Any conjectures?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd538fa8-26df-4f02-99a2-2faf56ef92ce%2F35b06f66-38bb-43a9-8658-958604c69ada%2Fcedwdk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the set
G = { [ D] + [J] ¹ + 1] +[3]},
where the entries of these matrices are in Z3. The operation is matrix multiplication.
(a) Prove that G is a group. (You can use the fact that matrix multiplication is associative.)
(b) Is G commutative or non-commutative?
(c) Recall that the order of an element g is the smallest positive exponent & such that
where e is the identity element in the group. Find the order of each element in G. Any conjectures?
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