You have a reference to a HOHOAOA, and need to de-reference it so:

use strict;
use warnings;

my $book = { 'key' => {'data' => [
                                      [ 'Element1',
                                        'Element2',
                                        'Element3'
                                      ],
                                      [ 'Element1',
                                        'Element2',
                                        'Element3'
                                      ]
                                    ]
                        }
           };
           
for my $key (keys %$book){
   for my $data (  keys %{ $book->{$key} } ){
       for my $inner_array_ref (   @{ $book->{$key}{$data} }  ) {
            ## Array above can also be written as: @{  $book->{$key}->
+{$data}  }
          print "$key\t$data\t@$inner_array_ref\n";    
       }
   }     
}
[download]