Select row, in which the value in one column corresponds to more different values in other column

I am trying to select rows from the table, where to one value in column A correspond both options in column C

The data is here:

A<-c(1,2,3,4,2,5,5,2,7,8)
B<-c(100,200,300, 50, 60,30,80,100, 90,1000)  
C<-c("X", "Y", "Y", "X", "Y", "Y", "X", "X", "Y", "Y")
data.frame(A,B,C)

And the result should look like this:

  A   B C
2 2 200 Y
5 2  60 Y
8 2 100 X
6 5  30 Y
7 5  80 X