another approach, with a few printing examples, also realize that something like $critters[1][2] is valid also.

#!/usr/bin/perl -w
use strict;
use Data::Dumper;

#I made the 2D array bigger as you only had one row

my @critters = ( ['a sheep', 'an elephant', 'the wolf'],
                 ['a fish',   'an eel',     'the whale']
               );
               
print "original array\n";
print Dumper \@critters;
             
my @articleList = ('the', 'an', 'a');
my $articleregex = join("|", @articleList);

print "one way to access the whale and a sheep\n";
print "$critters[1][2], $critters[0][0]\n";  #the whale a sheep

foreach my $rowref (@critters)  #each row
{
   foreach my $name (@$rowref)  #each "column" in that row
   {
       $name =~ s/^($articleregex) //;     
   }
}

print "\nmodified array:\n";
print Dumper \@critters;

print "\nPrint one row\n";
#when derefencing a thing with a subscript, you need to
#use {} to make clear what is being dereferenced, i.e. the
#entire row

print "@{$critters[1]}\n";

my $ref2arow = $critters[1]; #using an reference to a row
print "$ref2arow->[1]\n";    #print 2nd column (eel)

__END__
original array
$VAR1 = [
          [
            'a sheep',
            'an elephant',
            'the wolf'
          ],
          [
            'a fish',
            'an eel',
            'the whale'
          ]
        ];
one way to access the whale and a sheep
the whale, a sheep

modified array:
$VAR1 = [
          [
            'sheep',
            'elephant',
            'wolf'
          ],
          [
            'fish',
            'eel',
            'whale'
          ]
        ];

Print one row
fish eel whale
eel
[download]

Try adding prints in various places and play with this.