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Groups and Subgroups

  • Thread starter duki
  • Start date
  • #1
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Homework Statement



Thus far in my studying I've been able to at least have a sense of where to start solving the problems... until now.

Find the order of the subgroup of the multiplicative group G of 4x4 matrice generated by:

| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 1 0 |
| 1 0 0 0 |

Recall the identity e:

| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |

Homework Equations



The Attempt at a Solution



No clue, whatsoever. :(
 

Answers and Replies

  • #2
139
12
Call your matrix A. What's A3?
 
  • #3
264
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I'm not sure? =(
 
  • #4
Dick
Science Advisor
Homework Helper
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618
What do you mean, "I'm not sure"? Cube the matrix, i.e. multiply it by itself three times. Then you'll know what A^3 is. You aren't giving VKint the help deserved of the clue.
 
  • #5
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Ok, had to remember how to multiply matrices. I got the identity, e.
 
  • #6
Dick
Science Advisor
Homework Helper
26,258
618
So did I. Problem solved, right?
 
  • #7
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I don't quite understand. So is the order 3 because that's how many times I had to multiply it by itself to get the identity?
 
  • #8
Dick
Science Advisor
Homework Helper
26,258
618
A isn't the identity, A^2 isn't the identity, A^3 is. So yes, the order is 3. Look up 'order of a group element'.
 
  • #9
264
0
Awesome, thanks.
 

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