Can't add script even though the file name and the class name are the same

I was trying to test the script in Game mode but Unity just stated "All Compile Errors must be fixed". I removed the script from my Scene and I was able to enter the game mode. So the problem seems to be in the script.

I imported the same script back again and tried to attach it to Player sprite, but Unity now states: Can't add component 'Controls' because it doesn't exist. Please check if the file name and class name match.

So the filename is Controls.cs and here is the script:

using UnityEngine; using System.Collections;

public class Controls : MonoBehaviour {

 // Store the keys for players.
 public KeyCode moveUp;
 public KeyCode moveDown;

 // The speed is the same for both of the players so we can assign it here.
 public float playerSpeed = 10;
 
 // Update is called once per frame
 void Update () {
     if (Input.GetKey(moveUp)) {
         rigidbody2D.velocity.y = playerSpeed;
     } else if (Input.GetKey(moveDown)) {
         rigidbody2D.velocity.y = playerSpeed * -1;
     } else {
         rigidbody2D.velocity.y = 0;
     }
 }

}

I program several languages fluently but I have little experience with C#.