Important: Problem 3 is a continuation of Problem 2. It is very important that y
ID: 3168214 • Letter: I
Question
Important: Problem 3 is a continuation of Problem 2. It is very important that you have matching versions (A, B, C, etc.) of Problems 2 and 3. Check now to make sure you have matching versions. Problems 2 and 3 investigate the subset G of GL(2, C) listed below: 0 -1 0 11 -1 0 1 01 ;--c = 0 -il' o i -i 0 a. Fill in the Cayley Table below using matrix multiplication. Be careful with your computations; you will rely on them for this problem as well as Problem 3. Attach your work on separate paper. (This question is worth 8 points.) -e -e b. You don't need to worry about associativity since G is a subset of GL(2, C). Use your table to justify that G is a group. (This question is worth 2 points.)Explanation / Answer
e
-e
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e
e
-e
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-e
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e
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e
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e
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-e
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e
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-e
e
(b)Therefore The above table is a binary operation table. Hence 1. satisfied closure property
2.Associative property can be checked.
3. e is the identity
4.Inverses of e,-e,,-,,-,,- are e,-e,,-,,-,,- respectively. All are self inversed. Hence it is a group.
(c) H,H,H,H are left cosets
e
-e
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e
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e
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e
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e
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-e
e