The correct answer is A) Power that is recognized as legitimate
Authority is the power that is recognized as legitimate.
It is the right to give orders and enforce them. It is the faculty to make decisions and enforce action. Authority can be exerted by the people who have gained the right to do so. Legitimately. If that is not the case, then authority turns into tyranny that oppresses. A leader always has to exert its authority by example, not by coercion.