If Person A Is Represented By Person B and Person B Makes a Deal With Person C That Was Unauthorized By Person A, Then Is Person A Actually Obligated to Person C?
Generally, When An Agent Appears As Acting on Behalf of a Principal and Enters Into An Unauthorized Deal With a Third Party Person, the Principal Will Be Bound to the Deal.
Understanding the Principles of Agency Law Including the Required Conditions and Applicable Exceptions to the Rule
With only a few exceptions, when a business or a person is represented by an agent, and the agent is provided with a specific scope of authority; however, the agent thereafter enters into a deal that goes beyond the scope of authority, the basic principles of agency law will impose the deal upon the business or person who was represented by the agent.
"The general rule of agency is that a principal is bound by the acts of an agent when that agent is acting within the scope of his or her ordinary or apparent authority."
Supreme Court of Canada
Boma Manufacturing Ltd. v. CIBC,  3 SCR 727
The general principle of agency law whereby the principal becomes bound to the contracts agreed to by an agent, even an agent acting fraudulently or beyond the authority granted by the principal, is explained in many cases including Royal Bank of Canada v. Concrete Column Clamps (1961) Ltd., 1976 CanLII 192 (SCC),  2 S.C.R. 456 wherein the Supreme Court stated:
Agency law, especially as it relates to vicarious liability in tort, has long ago departed from strict conceptions of authority (see, for example, Limpus v. London General Omnibus Co.) and has, similarly, departed from notions of benefit or detriment so that an employer may be held vicariously liable to a person injured by his employee’s negligence, even though the employee has, while acting within the scope of his employment, carried out his duties in a way expressly prohibited by the employer: see, for example, Lockhart v. Stinson and C.P.R.; and cf. Rose v. Plenty.
Again, even where the employee defrauds a third person, his employer may have to answer for the fraud, as was the case in Lloyd v. Grace, Smith & Co., where a solicitor’s clerk, acting in the course of his employment, and held out as authorized to deal with clients of the solicitor, defrauded a client of her property. The principle underlying this and other cases is an old one, based on a broad rule of policy, stated for England nearly three hundred years ago in Hern v. Nichols and restated in fuller terms by the House of Lords in Lloyd v. Grace, Smith & Co., supra. There, Lord Shaw of Dunfermline put it as follows (at pp. 739-40):
The case is in one respect the not infrequent one of a situation in which each of two parties has been betrayed or injured by the fraudulent conduct of a third. I look upon it as a familiar doctrine as well as a safe general rule, and one making for security instead of uncertainty and insecurity in mercantile dealings, that the loss occasioned by the fault of a third person in such circumstances ought to fall upon the one of the two parties who clothed that third person as agent with the authority by which he was enabled to commit the fraud…
This Court too has recognized the principle, as witness The Queen v. Levy Bros. Ltd., at p. 192, where Ritchie J. quoted with approval the following passage from Story on Agency (7th ed.) para. 452:
…he (the principal) is held liable to third persons in a civil suit for the frauds, deceits, concealments, misrepresentations, torts, negligences, and other malfeasances, or misfeasances, and omissions of duty, of his agent, in the course of his employment, although the principal did not authorize, or justify, or participate in, or, indeed, know of such misconduct, or even if he forbade the acts, or disapproved of them.
Exception or Conditions to Principle
The exception to the general principle that a principal is bound to the agreements established by an agent are perhaps better stated as conditinos of the general principle whereas such are based upon the elements found within the general principle itself. Per Boma Manufacturing Ltd. v. Canadian Imperial Bank of Commerce, 1996 CanLII 149 (SCC),  3 S.C.R. 727 at paragraph 101 wherein it was said, "... The general rule of agency is that a principal is bound by the acts of an agent when that agent is acting within the scope of his or her ordinary or apparent authority. The agent does not cease to bind the principal when he or she acts fraudulently in furtherance of his or her own purposes. ..."; and accordingly, the general principle requires an ordinary or apparent authority to exist. If the agent is without an ordinary or apparent authority, then the principal is unbound by the actions of the agent.
The requirement of ordinary or apparent authority is often forgotten as key elements to the principle of agency and it should be remembered that the principle of agency is based upon a sense of fairness in that a third party person, who innocently believes that the agent is acting within the authority of the principal, deserves the protection of the law; and thus, the law finds against the principal who created the risk of improper conduct of the agent by engaging an agent. However, in circumstances where the third party person knew, or ought to know, that the agent is acting beyond the scope of authority granted to the agent by the principal, the third party person will lose the rule of agency benefit. Essentially, where the third party person is aware of the improper conduct of the agent, the third party person becomes a joint perpetrator, acting with the agent, to victimize the principal. This requirement that the third party person genuinely belief that the agent is acting within the authority of the principal as a condition of the general rule of agency was stated in Coutinho & Ferrostaal GmbH v. Tracomex (Canada) Ltd., 2015 BCSC 787 wherein it was said:
 I was advised by counsel for Imbamar that she had been unable to find any case law that addressed circumstances such as those that are present in this case. I am not surprised. It would be a curious result if third parties could rely on the assurances of an agent, known to them to be dishonest, in relation to the very transaction at issue, to bind an innocent principal.
 There is, however, considerable jurisprudence that militates against Imbamar’s position. First, the broad guidance provided in various relevant texts does not support Imbamar. In H.G. Beale et al, eds., Chitty on Contracts, 31st ed., (London, U.K.: Thomson Reuters, 2012), vol. 2, at para. 31-057, under the heading “Apparent Authority”, the authors note that a third party cannot hold a principal liable for the representations of an agent in circumstances where the third party “was put on inquiry by the facts of the transaction”.
 In Bowstead and Reynolds on Agency, 18th ed. (London, U.K.: Sweet & Maxwell, 2006), at para. 8-041, the author similarly confirms that the doctrine of apparent authority does not apply to a person who “is put on inquiry by the facts of the transaction.”
As to the point raised in Coutinho, the obvious question arises as to what constitutes as being, "put on inquiry by the facts of the transaction" to such a degree that the rule of agency fails to apply. The answer to this question is provided by the Court of Appeal within the case of Canadian Laboratory Supplies v. Engelhard Industries, 1977 CanLII 45 where it was said:
Where a transaction is of such an unusual nature that any reasonable person would be put on inquiry, a person cannot shelter under the doctrine of apparent authority. Houghton & Co. v. Nothard, Lowe & Wills, Ltd.,  1 K.B. 246.
Furthermore, and while it should go without speaking, where the third party is without innocence and is indeed colluding with the agent to participate in a wrongdoing against the principal, the third party is unable to hold the principal to the wrongful dealings by the agent. This exception to the rule of agency was stated in Barry v. Stoney Point Canning Co., 1917 CanLII 620, 55 S.C.R. 51 wherein it was said:
... any surreptitious dealing between one principal and the agent of the other principal is a fraud on such other principal ...
Generally, when a person is acting as another person, meaning when an agent is acting for a principal, such as when an employee acting for an employer, among other circumstances involving an agent acting as representation of a principal, the principal becomes bound to the agreements made by the agent so long as the reasonable person in a similar transaction would belief that the agent is acting within the authority of the principal.