The most straightforward way to do what you want is to use a hash to keep track of the elements that already exist, then scan the hash to determine duplicates. Something like:

#!/usr/bin/perl -w

use strict;

use vars qw(@all @dup);

@all=(["what", "is", "the", "matrix"],["matrix", "reloaded", "is", "no
+", "good"]);

my(%h1,%h2); # for the two halves of your array
grep { $h1{$_}=1 } @{$all[0]};
grep { $h2{$_}=1 } @{$all[1]};

@dup = ( [ map { $h2{$_} ? 1 : 0 } @{$all[0]} ],
         [ map { $h1{$_} ? 1 : 0 } @{$all[1]} ]);
print '([',
      join(',',@{$dup[0]}),
      '], [',
      join(',',@{$dup[1]}),
      "])\n";
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Oh, and map executes a block of code for each element in the array, returning an array consisting of the return value from each block of code.