use strict; identifies your error. Your getting the index of the last element in the array referenced by $array_ref, but $array_ref doesn't exist.

use strict;
use warnings;

my @array1 = qw(one two three four five);
my @array2 = qw(blue green white orange black);
my @array3 = qw(car bike plane ship);

my @array_of_refs = (\@array1, \@array2, \@array3);

print $#array_of_refs;          # 2
print $#{ $array_of_refs[2] };  # 3 = $#array3
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