I don't really know how to find the n-power matrix. I can't find a way.

A = (0, 1/2,0), (1, 0, 1),

(0, 1/2, 0)

And I know the power matrix is easy to find. But I can't think of an easy way to find this n-power matrix.

I would how you could find him.

Thanks for the help !

I hope it is readable. I'm sure you could easily prove this by induction. Keeps cycling between A and A^2. You can replace "n" with "n-1" and start n at 1 instead of 0. My A^0, A^1, A^2 in the boxes are out by 1. I didn't bother to re-do it.

Note that:

1) 1/4 + 1/4 = 1/2 and 1/4 - 1/4 = 0

2) 1/2 + 1/2 = 1 and 1/2 - 1/2 = 0