How to loop over an Array of Arrays as reference?

The below code works if $a is an Array of Arrays, but I need $a to be an reference to the Array of Arrays.

Question

How do I iterate through $a?

#!/usr/bin/perl

use warnings;
use strict;
use Data::Dumper;

my @AoA = ( ['aaa','hdr','500'],
            ['bbb','jid','424'],
            ['ccc','rde','402'],
            );

my $a = \@AoA;

my $s = "bbb";
my $d = "ddd";

for my $i ( 0 .. $#a ) {
    for my $j ( 0 .. $#{ $a[$i] } ) {
        if ($a[$i][$j] eq $s) {
            $a[$i][$j] = $d;
            last;
        }
    }
}

print Dumper $a;