# Stationary Process

I have some questions about stationary process and its statistical properties. If $\{X_t\}$ is a stationary process, then do the following equations hold? ($j$ is a integer)

$$\operatorname{E}[X_t]=\operatorname{E}[X_{t-j}]$$

$$\operatorname{Var}[X_t]=\operatorname{Var}[X_{t-j}]$$

Is $\{X_tX_{t-j}\}$ a stationary process?