Which of the following options is true for a linear time-invariant discrete time system that obeys the difference equation:
$$y\left [ n \right ]-ay\left [ n-1 \right ]=b_{0}x\left [ n \right ]-b_{1}x\left [ n-1 \right ]$$
- $y[n]$ is unaffected by the values of $x\left [ n-k \right ];k>2.$
- The system is necessarily causal.
- The system impulse response is non-zero at infinitely many instants.
- When $x\left [ n \right ]=0,n < 0$, the function $y\left [ n \right];n > 0$ is solely determined by the function $x[n]$.