my @array = @{ $key };
print join ",", @array;
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should be

my @array = @{ $reverse_translation{key} };
print join ",", @array;
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But that wastefully copies the array. Just work with the array reference:

my $array = $reverse_translation{key};
print join ",", @$array;
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Update: Oops, I missed the fact that you reversed the keys and values.

While the above does solve a problem, you are also running afoul of the restriction that hash keys (for untied hashes) can only be strings. When you attempted to use an array reference as a key, a string representation of the array reference was used as the key rather than the array reference itself. So when you tried to deference the keys, you were trying to dereference a string.

What are you trying to accomplish by reversing the hash? Would the following do?

foreach my $key (keys %translation) {
   print("$key: ");
   print(join(",", @{ $translation{$key} }));
   print("\n");
}
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