Which word best defines someone who is arrogantly domineering?

The term "imperious" precisely captures the essence of someone who is arrogantly domineering. It conveys a sense of commanding authority and superiority, often accompanied by an expectation of obedience without question. This word reflects an attitude of being overbearing and dictatorial, suggesting that the individual not only asserts control but does so in a condescending manner, which aligns with the description in the question.

In contrast, "fallow" refers to land that is left uncultivated, which does not relate to personal demeanor or behavior. "Impute" means to attribute a fault or responsibility to someone, and while it involves a judgment of sorts, it lacks the connotation of arrogance or domineering behavior. "Extirpate" means to root out or destroy completely, which pertains more to eradicating something rather than exhibiting a dominating personality. Therefore, "imperious" stands out as the most fitting choice, as it directly connects to the idea of someone who exudes an air of superiority and is commanding in a way that is both arrogant and domineering.