Question

The commander exercised his authority.
a. Transitive
b. Intransitive

Answer 1

is transitive because it uses his authority as a direct object

Answer 2

An action verb with a direct object is transitive while an action verb with no direct object is intransitive. Some verbs, such as arrive, go, lie, sneeze, sit, and die, are always intransitive; it is impossible for a direct object to follow.