To solve the given problem, let's trace the path taken by Arman step-by-step and determine his final position relative to his starting point, A. Then, we'll calculate the shortest distance and direction to return to point A.

1. Initial Position: Arman starts at point A.
2. Move South: He drives 32 km towards the south.
3. Take Left Turn (now facing East): He drives 37 km.
4. Take Left Turn (now facing North): He drives 35 km.
5. Take Left Turn (now facing West): He drives 38 km.
6. Take Left Turn (now facing South): He drives 3 km and stops at point P.

Let's visualize the above steps to determine the coordinates of point P relative to point A.

1. After driving 32 km south, the coordinates are (0, -32).
2. After turning left and driving 37 km east, the coordinates are (37, -32).
3. After turning left and driving 35 km north, the coordinates are (37, -32 + 35) = (37, 3).
4. After turning left and driving 38 km west, the coordinates are (37 - 38, 3) = (-1, 3).
5. After turning left and driving 3 km south, the final coordinates are (-1, 3 - 3) = (-1, 0).

Final Position (Point P): The coordinates are (-1, 0).

Point A is at the origin (0, 0). Thus, the shortest distance back to A is simply the horizontal distance:

Distance = \sqrt{((-1 - 0)^2 + (0 - 0)^2)} = \sqrt{1} = 1 \ \text{km}

Direction: Since point P is 1 km to the west of A, Arman needs to travel 1 km towards the east to reach point A.

Conclusion: To return to point A, Arman should drive 1 km to the east.

Therefore, the correct answer is "1 km to the east".