Impulse Response Descriptions for LTI Systems

If the impulse response of an LTI system is $h[n]$, what is the output of the system if the input is $x[n] = 2 \delta[n-3]$?

The impulse response of a system is given by $h[-1] = \frac{1}{3}, h[0] = \frac{1}{3}, h[1] = \frac{1}{3}$ with $h[n] = 0$ otherwise. Select all the statements that are true about this system.

The output of a system with input $w[n]$ and impulse response $z[n]$ is the same as the output of a system with input $z[n]$ and impulse response $w[n]$.