Find Order of Subgroup of 4x4 Matrices in G

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Homework Help Overview

The discussion revolves around finding the order of a subgroup within the multiplicative group of 4x4 matrices, specifically focusing on a given matrix and its powers.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the concept of matrix multiplication and the implications of raising a matrix to a power to determine its order. Questions arise about the relationship between the number of multiplications and the resulting identity matrix.

Discussion Status

Participants are actively engaging with the problem, with some providing hints and guidance on how to approach the matrix multiplication. There is a recognition of the importance of understanding the order of the matrix in relation to the identity matrix.

Contextual Notes

Some participants express uncertainty about the calculations involved in matrix multiplication and the concept of order in group theory. The original poster indicates a lack of initial understanding, which prompts further exploration and clarification from others.

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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. :(
 
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Call your matrix A. What's A3?
 
I'm not sure? =(
 
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.
 
Ok, had to remember how to multiply matrices. I got the identity, e.
 
So did I. Problem solved, right?
 
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?
 
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'.
 
Awesome, thanks.
 

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