Is it possible for the front and rear references in a circular array implementation to be equal?

Yes it is possible for the following cases:-

Explanation:

When the queue is full the the front and the rear references in the circular array implementation are equal because after inserting an element in the queue we increase the rear pointer.So when inserting the last element the rear pointer will be increased and it will become equal to front pointer.

When the queue is empty the front and rear pointer are equal.We remove an element from queue by deleting the element at front pointer decreasing the front pointer when there is only one element and we are deleting that element front and rear pointer will become equal after deleting that element.