How big are the arrays? If they are small then you could:

use warnings;
use strict;

my %hoa = (
    array1 => [ 1,2,3 ],
    array2 => [ 7,8,9 ],
    array3 => [ 1,2,3 ],
    array4 => [ 7,8,9 ],
    array5 => [ 9,9,9 ],
    array6 => [ 1,2,3 ],
);
my %dups;

push @{$dups{join '~', @{$hoa{$_}}}}, $_ for sort keys %hoa;
print map {join (" ", @{$dups{$_}}), "\n"} grep @{$dups{$_}} > 1, keys
+ %dups;
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Prints:

array1 array3 array6
array2 array4
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