Time Invariance
If the cascade
x(t)--->[time delay by t0]----->[system]-----z(t) ---(1)
yields the same output as the reverse of (a);x(t)--->[system]--->[time delay by t0]---y(t), it is called Time invariant.
Prove
x(t)--->[system]-->y(t)=2x(t)
x(t)--->[time delay by t0]--->y(t)=x(t-t0)----->[system]---->z(t)=2x(t-t0) ---(1)
x(t)--->[system]--->y(t)=2x(t)---->[time delay by y0]---->z(t)=2x(t-t0) ---(2)
The results of (1) and (2) are the same. Thus, it is time invariant.
