Check which rows in a data.table are identical

I need a solution that shows me which rows are identical but I can't find a clever solution (a solution without a bunch of complex loops). I would prefer a data.table solution. What I want to have is a list with line numbers that have the identical entries.

An example:

library(data.table)
Data <- data.table(A = c("a", "a", "c"), 
                   B = c("A", "A", "B"))

The first and the second line are identical. My desired output:

[[1]]
[1] 1 2

[[2]]
[1] 3