I am trying to see if
y[n] = [cos(πn)]x[n]
is casual, stable, linear and shift-invariant.
I came up with the solution that it is not stable since it is not "summable" (As my professor says). I took the limit of cos(πn) (correct me if that method is wrong)
For the causal part, I learned that for it to be non-causal, the output depends upon future inputs. I believe that this is non-causal since there are no present or past inputs.
for Linearity: I said it was linear, but I am not sure on this one.
for shift-invariance I stated that this system was indeed invariant