You haven't defined $ligand anywhere (if you had warnings and strict turned on, perl would've complained about that), yet you use it as the hash key. I'm not sure how your hash ends up with more than a single pair in it!

I would rewrite the meat of your code as follows:

# @key_set and @val_set are my names for @A1 and @A2
# there is no need to shuffle them!

my %pairs;
my $size = 100;  # from the user
until (keys(%pairs) == $size) {
  my $key = $key_set[rand @key_set];
  my $val = $val_set[rand @val_set];
  $pairs{"$key-$val"} = 1;

  # or even just:
  # $pairs{$key_set[rand @key_set] . "-" . $val_set[rand @val_set]} = 
+1;
}

for (keys %pairs) {
  print "$_\n";
}
[download]

This seems to fulfill your goal.