By "member array ref" of an AoA you can understand two things:

1. The "member array ref" points to the same memory object as the element in the AoA points to.
2. The "member array ref" points to a different memory object which has an identical "printable representation", or other criterion of comparison you may see fit.

From your post, I assume you want (2). Here's an implementation of both (1) an (2) together with a test. Be aware that my implementation of (2) is simple - it relies on stringification by joining with $;, which does not work if the arrays in the AoA are themselves deep data structures and may give incorrect results if you use the value of $; in your subarray values.

#!/usr/bin/perl

use strict;
use warnings;

sub member_as_object {
  my $aref = shift;
  my $AoAref = shift;

  return grep {$aref eq $_} @{$AoAref};
}

sub stringify {
  return join $;, @{(shift)};
}

sub member_as_stringified_value {
  my $astring = stringify(shift);
  my $AoAref = shift;

  return grep {$astring eq stringify($_)} @{$AoAref};
}


# building a test case below

my @AoA = (
       [ 'beethoven', 'berlioz', 'strauss' ],
       [ 'wagner',    'mozart',  'brahms' ],
       [ 'sibelius',  'elgar',   'dvorak' ]
      );

my %arrays = (
        member_obj  =>  $AoA[1],
        member_copy =>  [ @{$AoA[1]} ],
        non_member  =>  [ qw/foo bar baz/ ]
       );

my %compare_subs =
  (
   member_as_object => \&member_as_object,
   member_as_stringified_value => \&member_as_stringified_value
  );

for my $csub (sort keys %compare_subs) {
  for my $array (sort keys %arrays) {
    my $result =
      $compare_subs{$csub}->($arrays{$array}, \@AoA) ? 'true' : 'false
+';

    print "$csub($array) = $result\n";
  }
}
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