1. (a) That's right. This concerns a principal's power to decide, on their own, to end the agent's authority. This is something the law generally allows a principal to do. The principal can revoke an agent's power simply by notifying the agent of their decision. The notice can be oral, even if the agent's original authority was given in writing. However, it is important to note that a principal's revocation of the agent's authority may be a breach of contract, giving the agent a right to claim damages. In the present case, A has the power terminate B's agency, but will most likely be liable to B for breach of contract.
NOTE 1: Just as the principal can act unilaterally to revoke an agent's authority, the agent can decide to renounce their authority, by telling their principal that they no longer intend to carry out the mandate. Doing so is effective even if it amounts to a breach of the contract with the principal, in which case the principal may have a claim for damages against the agent.
NOTE 2: Some legislative provisions exist that govern various aspects of a principal's power to revoke an agent's mandate, e.g. to protect the interests of third parties who may have dealt with the agent without notice of the revocation.