For existence identity element 'e' :
x op e = e op x = x
Here x op y = x + y - 2
So x op e = x + e - 2 = x [ As mentioned above ]
==> e = 2
Now e op x should also yield the same identity element , else identity element does not exist..
So e op x = e + x - 2 = x
==> e = 2
Hence in both cases we get e = 2 and hence 2 is the required identity element..
Now for finding inverse , say y w.r.t x :
x op y = e
==> x + y - 2 = 2
==> y = 4 - x
Hence C) should be the correct answer..
