Just two things I can be bothered commenting on:

Prints:

1. while (chomp($line = <IN>)) will not work as you expect. Read the chomp documentation
2. use sensible identifiers and at least fix the strictures errors before you post.

     use strict;
     use warnings;

     open(IN, "list.txt") or die;
     chomp($line = <IN>);
     ($element, @abc) = split /\s+/, $line;
     while (chomp($line = <IN>)) {
     ($values, @xyz) = split /\s+/, $line;
     for ($i=0; $i<@xyz; $i++) {
     $s{$values}{$abc[$i]} = $xyz[$i];
        }
    }
    close(IN);
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I made the identifiers sensible, but I am not sure what to assign as a explicit package for i, lines 6-10. My understanding is that it should get that information from the file being invoked.

Your code and logic is rather convoluted.

I offer:

use strict;
use warnings;

my %element;
while (<DATA>){
  my ($elem, $value) = split;
  $element{$elem}= $value;
}
print "  ";
print "$_ " for sort keys %element;
print "\n";
for my $k1(sort keys %element){
  print "$k1 ";
  for my $k2(sort keys %element){
     my $val = $element{$k1} eq "X" ? 0
             :  $element{$k2} eq "X" ? 0
             : 2;
     print $val . " ";
  }
  print "\n";
}

__DATA__
  A X
     B Y
     C Z
     D X
     E X
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             I hope life isn't a big joke, because I don't get it.
                   -SNL

Can you please show the output you get when you run this code?

I didn't test NetWallah's solution, but I thought I'd take a sec to try to help you understand why we know you didn't test your own code, and show you a couple more updated approaches to writing Perl.

You should use the three argument form when opening a file, and be ready to spit the reason if the open fails, like this:

open my $fh, '<', 'list.txt' or die "Can't open list.txt: $!";
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Note that I used a scalar ($fh) to accept the File Handle instead of a bareword ('IN', in this case). The '<' signifies that the file is to be opened in read-only mode.

Also, if you ran your code, you would have found that under the 'strict' pragma, you need to make your declared/defined variables lexical. Most commonly, we'd use 'my' to do so:

my ( $a, @ss ) = split ...
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One last thing... within a while loop when iterating through a file, it is idiomatic to write it like this (note the 'my'):

while ( my $line = <$fh> ){
    chomp $line;
    print "$line\n";
}
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I didnt get your question in the first place. The confusion here is the data you gave is

A X
     B Y
     C Z
     D X
     E X
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where A has X, B has Y, C has Z .... But, the output you showed is a 3x4 matrix. Can you elaborate the question? (especially the correlation between the given data and the output you desired)

I would appreciate any input on 1) code correctness

use strict;
use warnings;

open(IN, "list.txt") or die;
chomp($line = <IN>);
($a, @ss) = split /\s+/, $line;
while (chomp($line = <IN>)) {
    ($aa, @prs) = split /\s+/, $line;
    for ($i=0; $i<@prs; $i++) {
$s{$aa}{$ss[$i]} = $prs[$i];
    }
}
close(IN);
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use strict;
use warnings;

open my $IN, '<', 'list.txt' or die "Cannot open 'list.txt' because: $
+!";
my ( undef, @ss ) = split ' ', <$IN>;
my %s;
while ( <$IN> ) {
    my ( $aa, @prs ) = split;
    @{ $s{ $aa } }{ @ss } = @prs;
}
close $IN;
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