Finding autocorrelation matrix of an autoregressive process AR(1)
Hi: You're expression will be a 3 by 3 matrix with the 1's along the diagonal and the correlations in the respective places.

$\begin{matrix}  1 &amp; \sigma_{12} &amp; \sigma_{13}  \\ 
                 \sigma_{21} &amp; 1 &amp; \sigma_{23}  \\
                 \sigma_{31} &amp; \sigma_{32} &amp; 1 
\end{matrix}$

The 12 and 21 elements are $\rho$   because the lag one autocorrelation of an AR(1) with parameter $\rho$ is $\rho$.  

The 23 and 32 elements are also $\rho$  for the same reason as above:  The lag one autocorrelation of an AR(1) with parameter $\rho$ is $\rho$.  

The 13 and 31 elements are $\rho^2 $  because the lag 2 autocorrelation of an AR(1) with parameter $\rho$ is $\rho^2$.  

The transfer function implies that $\rho = 0.7$. This is because 

$ y_t = \rho \times y_{t-1} + \epsilon_t$ has transfer function $H(z) =
\frac{1}{(1-\rho z^{-1})}$.