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Seeking help on permutation

Let say, I have a character vector of arbitrary length:

Vector <- c("a", "b", "c")

Using that vector I would like to create a matrix (with number of columns as 2) with all pairwise combinations of those elements, like:

Vector <- c("a", "b", "c")
Mat ? ? <- rbind(c("a", "b"), c("a", "c"), c("b", "c")); Mat ?# number of rows will obviously be n(n-1)/2
? ? ?[,1] [,2]
[1,] "a" ?"b"?
[2,] "a" ?"c"?
[3,] "b" ?"c"?


Order must be kept same as?c("c", "a") or c("c", "b")?would not be allowed. Additionally, actually I have a very big initial character vector therefore I need to maintain speed as well.

I would be really?grateful?if somebody guide me how to do that