A politician has a strong personality that inspires obedience among the public. What type of leader is this?

authoritative

charismatic

rational-legal

traditional

The correct answer should be authoritative

Strong personality that inspires obedience is what being authoritative is about. Charismatic leaders usually don't have strong personalities but are more about wits and likability and similar things which is another way to inspire support, but getting respect is more about being authoritative.

Authoritative is what I would say honestly