Show some working and we can help better. Here is a general way that I would recommend approaching this problem.

1) Calculate a few powers of A and try to spot a pattern.

2) Use your findings to speculate what the nth power would be.

3) Show that your formula works when n = 1.

4) Show that if your formula holds for n=k, then it also holds for n=k+1.

5) Smile, because your speculation was correct and you have just proved it by induction.

Let us know which step you get stuck on.