2. (a) That's probably wrong. It may be that Z has no express authority to purchase office supplies on behalf of the company. But it is possible for a person to be vested with an authority to represent another by implication rather than expressly. In particular, an agent will have an implied authority to do anything that is necessarily or normally incidental to acts that are expressly authorised. An agent will also have implied authority to do anything that agents usually do when employed in a particular capacity (such as a manager). And agents also have implied authority to do whatever an agent employed in the particular market or business customarily has authority to do.
Why should this be so? Because it is reasonable and convenient to infer that, in the different circumstances described, an agent has the necessary, usual or customary authority. In such circumstances, the employer (principal) is bound by an agent who acts in terms of an implied authority just as if that authority were expressly given. In the present case, it is likely that the purchase of office supplies is a necessary part of Z's authorised powers as office manager. In addition, Z would have 'usual' authority to purchase office supplies. Clearly, she has acted within this implied authority and A would be bound to accept and pay for the supplies.