I need to prove by induction that this 2x2 matrix:

[cosθ -senθ; senθ cosθ]^n is equal to this 2x2 matrix:

[cos(n)θ -sen(n)θ; sen(n)θ cos(n)θ] for all n ∈ Z.

Since it's by induction, I've already got the $\displaystyle n = 1$ and $\displaystyle n = k$, but... now what?

Thanks!