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

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