Let A = [1/2 -1/2; -1/2 1/2]

Computer A^2 and A^3. What will A^n turn out to be?

I computed A^2, how can I computer A^3? Is it possible to just multiply the product of A^2 with another A? That doesn't seem right to me though. And I have no idea how to find A^n. Thanks for the help!