What about this?
string s = new string((
from c in "ABCdef"
select char.IsUpper(c) ? char.ToLower(c) : char.ToUpper(c)
Note by Alexander Bell: In regards to the performance, this one (i.e. Alternate 9) is the worst in comparison with Alternate 1 and Alternate 2, also it requires Linq Library, which negatively impacts the Algorithm portability: Alternate 9 is NOT RECOMMENDED