Check to see whether it is time invariant or not?

[chessmath]

Hi
the problem that I am dealing with is to check whether y[n]=T{x[n]}=x[kn] time invariant or not?

My solution is I said z(n)=T{x[n-A]}=x[k(n-A)]

and y[n-A]=x[k(n-A)]
and because y[n-A]=z(n) so it is time invariant

but solution is saying that it is time varying because z(n)=x[kn-A] meaning that A is not multiplied by n so y[n-A] is not equal to z(n).

Can anyone explain to me why this is the case?
Thanks

 

[rude man]

The gain is obviously a function of time. As n (which means as time) increases, so does the gain of the system - ad infinitum. Example: x[n]) = 1 for all n, then y[n] = k, 2k, 3k, ... so the system gain increases forever.