An owner wants to net $$8,000$ on the sale of his small vacant lot. He gives a broker an option to buy the lot at that price or nominate a purchaser. The broker pays $$800$ for the option. Before the option expires, the broker sells the property to a third person for $$9,200.$ The broker advised the buyer during the negotiations that she was the optionee. Which of these is a TRUE statement?

A$.$ The broker is guilty of fraud.

B$.$ After paying the appropriate closing costs, the broker may keep the amount of money above and beyond the option purchase price of $$8,000.$

C$.$ The broker is guilty of violating her fiduciary relationship with the owner.

D$.$ The broker has violated Chapter $475,$ Florida Statutes.