#!/usr/bin/perl

# http://perlmonks.org/?node_id=1168667

use strict;
use warnings;

my $file1 = <<END;
A   1_1
A   1_2
B   1_3
C   1_4
END

my $file2 = <<END;
A   2_1
B   2_2
END

"$file1\0\n$file2" =~
  /
  ^(\S+)\ +(\S+)\n
  .*
  \0\n
  .*?
  ^(\S+)\ +(\S+)\n
  (?{ print
  "$1 from FILE1 with number $2 and $3 from FILE2 with number $4 ",
    $1 eq $3 ? "match" : "DO NOT match", "\n"
  })
  (*FAIL)
  /msx;
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prints your desired output