Product of matrices representing rotations

Question

I am trying to prove that, given $n\in \mathbb{N}$, the matrix $R_1=\begin{pmatrix} \cos(\frac{2 \pi} {n}) &-\sin(\frac{2 \pi} {n}) \\ \sin(\frac{2 \pi} {n}) & \cos(\frac{2 \pi} {n}) \end{pmatrix}$ and the matrices $R_j=R_1^j \quad\forall j=0,1,\cdots, n-1$, then $R_jR_k=R_{(j+k) \pmod n} $. I have already showed that,by using the trigonometric identities for the sum of angles, $R_j$ represents a rotation of anngle $\frac{2 \pi j} {n} $. Moreover, by the properties of rotations, $R_jR_k=R_{\frac{2\pi(j+k)}{n}}$ But, at this point, I don't know how to conclude the desired equality. Appreciate any help.