First off, there is a set of functions that will generate the HTML for you, in the CGI module. As it stands, your code doesn't emit well-formed HTML.

But, to use that set of functions, you need to change your data structure into something that is more easily handled. Warning - the variables are poorly named. But, it is tested.

my @x;
my $curr = '';
my @curr;
foreach my $ref (@$matrix_ref)
{
    my $k = $ref->[0] . $ref->[1];
    unless ($curr eq $k)
    {
        push @x, [ @curr ] if @curr;

        @curr = @$ref;
        $curr = $k;

        next;
    }

    push @curr, $ref->[2];
}
push @x, [ @curr ];

use CGI qw( :all );

$html_str = table( map { Tr( td( $_ ) ) } @x );
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