It may be best to work on the A.txt and B.txt data sets you showed. If you can create a script to generate the ORed results of those two matrices, then it's most likely that script will work with larger matrices.

First, always begin your scripts with either:

use strict;
use warnings;
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or

use Modern::Perl;
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I prefer the latter, since it includes the former two pragmas--among other things.

You can use File::Slurp qw/read_file/; to read a file's contents into an array. The foreach() takes a list or array--not a scalar, like you've done. That would account for some of the errors.

Here's one way to approach the problem:

1. Read both matrix files into arrays.
2. The first element (row 0) of each array is identical, as it contains the column titles. Grab those and create the title string (like in the first script, but w/o sorting), and move to the next rows (1 .. n) of the two arrays.
3. Split each row (1 .. n) of the two arrays into their elements, placing those elements into two element arrays. The zeroth element of these arrays contains the row label.
4. Do an OR comparison between the two element arrays (1 .. n), and build an OR-result array for the table.
5. Finally, build the table and print it.

The scripting that produced the first table should help with reading files and building the table.

Step through this scripting process, and then share what you've completed. A script can be created to produce the ORed output you need; it'll just take a little more work...