What Is the Difference Between Authority and Influence

What is the difference between authority and influence?

A) Authority is the informal ability to convince people to act in a certain manner, whereas influence is the formally recognized ability to direct people's actions.
B) Authority is the formally recognized ability to direct people's actions whereas influence is the informal ability to persuade people to act in a certain manner.
C) Influence is always backed by formal sanctions such as policing and law.
D) Elder men in a society hold authority whereas people of any age or gender can hold influence.