Relation between matrixes problem

[essif]

Hi, I have a problem with an argument here.

I am given 4 Matrixes, A, C, D and F. see attachment..

I can then see that A^n = C*D^n*F = some matrix with a Fibonacci-serie in it.

I can also see that C*F=F*C=I or C is the inverse of F

My problem is to relate these two:
How can the fact that C is the inverse of F explain that A^n = C*D^n*F ?

NB. A^n = C*D^n*F is NOT true for any two C and F, C^-1=F, which in my mind make it even harder to see the relation.

 

[Tomsk]

I can't see the attachment, but I'm guessing this is to do with the idea that A^n = (CDF)^n = (CDF)(CDF)(CDF)(CDF)...(CDF) = CD(FC)D(FC)D(FC)D(FC)D(FC)D...DF = CDIDIDIDIDIDID...DF = CDDDDD...DF = CD^nF

I'm afraid I'm not quite sure what it is you're stuck on, but hopefully that will help.

 

[essif]

I think that's it, thanks alot.