I have a data.frame that looks like this (however with a larger number of columns and rows):

I want to sum the rows that have all columns identical and create last column "count", in order to get something like this:

Thank you for help!
data:
structure(list(Gene = c("A", "A", "B", "C"), `Cell 1` = c(2,
2, 3, 4), `Cell 2` = c(2, 2, 3, 4), `Cell 3` = c(2, 2, 3, 4)), row.names = c(NA,
-4L), class = c("tbl_df", "tbl", "data.frame"))
>