sub AS_ARRAY {
    my $self=shift;
    # do something useful here
}

##</code><code>##

$obj->[42];  # would be the same as
$obj->AS_ARRAY(42);  # and so on...

##</code><code>##

@$m # entire matrix, your syntax: $m->()
$m->[ 1] # second row, your syntax $m->( 1);
$m->[ 1]->[ 0] # individual element, your syntax $m->( 1, 0);

##</code><code>##

package Matrix;
use strict; use warnings;

use Scalar::Util qw/refaddr/;
use Data::Dumper;

use base 'Exporter';
our @EXPORT='matrix';

use overload (
    '""'  => 'stringify',
    '*'   => 'mult',
    '*='  => 'multby',
    '**'  => 'pow',
    '&{}' => '_code',
);

sub matrix { Matrix->new(@_) }

sub mkaoa { [[ @_[0,1] ], [ @_[2,3] ]] }

{
    my %entry;
    my %code;

    sub entry : lvalue {
        my $id=refaddr shift;
        @_==0 ? $entry{$id} :
        @_==1 ? $entry{$id}[ $_[0] ] :
                $entry{$id}[ $_[0] ][ $_[1] ];
    }

    sub _code : lvalue { $code{ refaddr shift} }

    sub DESTROY {
        my $id = refaddr shift;
        delete $entry{ $id};
        delete $code{ $id};
    }
}

sub new {
    my $class = shift;
    my $self = bless( \ my $o, $class);
    $self->init(@_);
}

sub init {
    my $obj=shift;
    $obj->_code = sub : lvalue {
        $obj->entry(@_);
    };
    $obj->() = mkaoa @_;
    $obj;
}

sub stringify {
    my $m = shift;
    "[[@{ $m->( 0) }] [@{ $m->( 1) }]]";
}

sub _mult {
    my ($s,$o)=@_;
    my $code = $s->_code;
    $s->(0,0)*$o->(0,0) + $s->(0,1)*$o->(1,0),
    $s->(0,0)*$o->(0,1) + $s->(0,1)*$o->(1,1),
    $s->(1,0)*$o->(0,0) + $s->(1,1)*$o->(1,0),
    $s->(1,0)*$o->(0,1) + $s->(1,1)*$o->(1,1);
}

sub mult {
    my ($s,$o)=@_;
    matrix $s->_mult($o)
}

sub multby {
    my ($s,$o)=@_;
    $s->() = mkaoa $s->_mult($o);
    $s;
}

sub pow {
    my ($self, $n) = @_;
    my $out = matrix 1,0,0,1;
    if ( $n < 6 ) {
        $out->multby( $self) for 1 .. $n
    } else {
        my $pow = matrix map @$_, @{ $self->() }; # clone $self
        while ( $n ) {
            $out->multby( $pow) if $n & 1;
            $pow->multby( $pow);
            $n = int $n/2;
        }
    }
    $out;
}

1;

__END__