I would recommend trying `Readonly'.

use Readonly;

Readonly my @readonly => (['book', 'pen', 'pencil'],
                          ['bat', 'ball', 'glove'],
                          ['snake', 'rat', 'rabbit']);

print $readonly[0][0], "\n";

$readonly[0][0] = "comicbook";

1;
[download]

Outputs the following:
book
Modification of a read-only value attempted at ./readonly.pl line 11
Plus you should be able to fill in the array at runtime so that should give you more flexibility.