Find Order of Subgroup of 4x4 Matrices in G

[duki]

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. :(

 

[VKint]

Call your matrix A. What's A³?

 

[duki]

I'm not sure? =(

 

[Dick]

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.

 

[duki]

Ok, had to remember how to multiply matrices. I got the identity, e.

 

[Dick]

So did I. Problem solved, right?

 

[duki]

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?

 

[Dick]

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'.

 

[duki]

Awesome, thanks.