(a) That's right. An Australian Business Number (ABN) is a number that is used to identify a business when dealing with other businesses or government agencies. It is easy to use an ABN to look up information about a business.
A sole trader is entitled to obtain an ABN and it can be a disadvantage not to have one. An ABN is a convenient way for a business to identify itself when dealing with suppliers and customers. It also means that persons making payments to the business are not required to withhold a portion of the payment against taxes. Having an ABN is also a requirement for various other things, such as registering a domain name.