Getting pairwise differences

[roroba]

I am trying to get pairwise differences for price between localities. My data look like this:

  table=NULL
  table$id= 1:9
  table$locality= c("A", "B", "C")
  table$price= rnorm(9, 444, 322)
  table$concat=paste(table$id, table$locality)
  final=data.frame(table)
  final

id locality    price concat
 1        A 379.1501    1 A
 2        B 792.3608    2 B
 3        C 762.0627    3 C
 4        A 439.0378    4 A
 5        B 100.2860    5 B
 6        C 830.2024    6 C
 7        A 148.5925    7 A
 8        B 668.3819    8 B
 9        C 510.3919    9 C

My goal is get if its possible get a table like this variable, in my below table concat is id:

diff_A-B | diff_A-C | diff_B-C
1A-2B  |  1A-3C   |  2B-3C
1A-5B  |  1A-6C   |  2B-6C
1A-8B  |  1A-9C   |  2B-9C
4A-2B  |  4A-3C   |  5B-3C
4A-5B  |  4A-6C   |  5B-6C
4A-8B  |  4A-9C   |  5B-9C
7A-2B  |  7A-3C   |  8B-3C
7A-5B  |  7A-6C   |  8B-6C
7A-8B  |  7A-9C   |  8B-9C

I tried:

library(dplyr)
table %>%
arrange(id, locality) %>% 
group_by(concat) %>%
mutate(variables=outer(price,price, "-"))

But the output doesn't show me the results that I need.

Please any advice will be appreciated.