ln question

[Jumbler_Chi at mobitai.com.tw]

Hi hackers !

I have one strange thing about 'ln' command.
my box is 5.2R.
I built some directory on $HOME , such as $HOME/a/b
I want to create  a symbolic link for 'b'  under top directory , $HOME.

so , I typed some command as

$ mkdir $HOME/a
$ mkdir $HOME/a/b

$ cd $HOME/a
$ ln -s b ../
$ cd $HOME/b
cd: can't cd to /home/matrix/b
$ file $HOME/b
b: broken symbolic link to b

but  when I also created another symbolic link as following again , it is
ok.  why is it broken symbolic link?!
$ rm $HOME/b
$ rmdir $HOME/a/b
$ rmdir $HOME/a

$ mkdir $HOME/a
$ mkdir $HOME/a/b
$ cd $HOME
$ ln -s a/b .
$ cd $HOME/b


Regards!!

Jumbler