"ORA-01017: invalid username/password" : Why is that?
SYSDBA isn't a user but a way to connect to the DB.  

Connecting as sysdba is based on the OS authentication which means that as long as you connect to your machine with a user which is in the oradba group you will be connected with this user AS SYSDBA no metter what user/password you'll write (as long as you try to connect as sysdba of course)

Read more in this Tom Kyte's thread

So, this-

SQLPLUS / AS SYSDBA


and this

SQLPLUS a/b AS SYSDBA


and even this

SQLPLUS
Enter user-name: as SYSDBA
Enter user-name: a
Enter password: b


Are pretty much the same