AR: $\epsilon_t=\rho\epsilon_{t-1}+\eta_t$ with $\eta_t $ i.i.d. $N(0, \sigma^2), t=1,...,n$ and $\epsilon_0=0$ with $\eta_0\sim N(0,\frac{\sigma^2}{1-\rho^2}),\lvert\rho\rvert<1;$
Why is the variance of $\eta_0 = \frac{\sigma^2}{1-\rho^2}$? Is it correct to assume Var$(\epsilon_{t-1})=\sigma^2$?