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**confused!!..system stability and linearity**

1)-Is y(n)=cos{x(n)} a stable system??

and is the condition s=Ʃ|h(k)|<∞ for stability valid only for LTI systems?

actually my book solves the given problem using the above method..but according to me the given system is not LTI SINCE ZERO I/P does not lead to zero O/P...so i m really confused

2)to prove system to be linear is it enough to pove that zero i/p leads to zero o/p??

the system y(t)=[{x(t)}^2] also gives zero o/p on zero i/p but it is not linear...