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# FP1 Matrices Watch

It's Question 5(c) from AQA FP1 June 2006.
http://filestore.aqa.org.uk/subjects...W-QP-JUN06.PDF

Have found M^2 as
[0 1]
[-1 0]

and M^4 as
[-1 0]
[0 -1]

but haven't got a clue how to go about finding M^2006, any help greatly appreciated.

(Sorry for lack of latex!)
2. (Original post by Vernish)
but haven't got a clue how to go about finding M^2006, any help greatly appreciated.

(Sorry for lack of latex!)
Work out M^8,

Then what's M^(k8) for any postive integer k.

Can you take it from there?
3. OK,
M^8 is identity matrix, so M^(k8) is the identity matrix?
M^2000 is the identity matrix, so I need M^6. Which would be
[0 -1]
[1 0]

which is what they've got in the mark scheme

Thank you very much!!
4. (Original post by Vernish)
OK,
M^8 is identity matrix, so M^(k8) is the identity matrix?
Yep.

M^2000 is the identity matrix, so I need M^6. Which would be
[0 -1]
[1 0]

which is what they've got in the mark scheme

Thank you very much!!
You're welcome.

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