What you called "CABABILITIES", I called "roles" for short.
That which has "CABABILITIES", I called "actor".

Instead of building a hash of roles by actor, build a hash of actors by role. That way, your data structure will ressemble your output. (Update: Oops, that is what you are doing. The rest of the post applies, though.)

In the code below, I replaced doing the same thing to three different arrays with a single loop.

use strict;
use warnings;

my @arrays = (
   [ qw( A 1 2 3 4 5 ) ],
   [ qw( B 1 2 5 6   ) ],
   [ qw( C 2 3       ) ],
);

my %actors_by_role;
foreach my $array (@arrays) {
   my ($actor, @roles) = @$array;
   foreach my $role (@roles) {
      push @{$actors_by_role{$role}}, $actor;
   }
}

my @roles = sort keys %actors_by_role;

foreach my $role (@roles) {
   print(join("\t", $role => sort @{$actors_by_role{$role}}), "\n");
}
[download]

Output:

1       A       B
2       A       B       C
3       A       C
4       A
5       A       B
6       B
[download]

From there, it's not hard to get the second output.

use strict;
use warnings;

my @arrays = (
   [ qw( A 1 2 3 4 5 ) ],
   [ qw( B 1 2 5 6   ) ],
   [ qw( C 2 3       ) ],
);

my %actors;
my %actors_by_role;

foreach my $array (@arrays) {
   my @roles = @$array;
   my $actor = shift(@roles);

   $actors{$actor} = 1;

   foreach my $role (@roles) {
      $actors_by_role{$role}{$actor} = 1;
   }
}

my @roles  = sort keys %actors_by_role;
my @actors = sort keys %actors;

{
   foreach my $actor (@actors) {
      print("\t", $actor);
   }
   print("\n");
}

foreach my $role (@roles) {
   print($role);
   foreach my $actor (@actors) {
      print("\t", $actors_by_role{$role}{$actor} ? 'X' : ' ');
   }
   print("\n");
}
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Output:

        A       B       C
1       X       X
2       X       X       X
3       X               X
4       X
5       X       X
6               X
[download]