ow to create an anonymous array for each line and store a reference to that array in the hash?

Anonymous arrays are created with [ ], see perlref

But there is no need to do that, the problem you describe does not happen

my %hash;
for my $eye ( 0 .. 2 ){
    my @file_lines = map { "$eye$_" } 'a'..'c';
    $hash{$eye} = \@file_lines;
}
use Data::Dumper;
print Dumper( \%hash );
__END__
$VAR1 = {
          '1' => [
                   '1a',
                   '1b',
                   '1c'
                 ],
          '0' => [
                   '0a',
                   '0b',
                   '0c'
                 ],
          '2' => [
                   '2a',
                   '2b',
                   '2c'
                 ]
        };
[download]

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