singleton pointer and updating variables of the singleton with the pointer

When i have created a player class and created a singleton in it:

public static Player instance;

 void Awake()
 {
     if (instance != null)
     {
         Debug.LogWarning("More than one instance of Inventory found");
         return;
     }
     instance = this;
 }

one variable in Player class is playerData and in player data where is a variabale inventory (array of items). in the inventoryUpdate scrip i want to change the items in the inventory that is in the player class . I don't want to call the class every time i want to change (not to call Player.playerData.inventory every time) I tried to point on the inventory variable and call it on Create local variable inventory and that will point on inventory in Start(){inventory = Player.playerData.inventory;} but the playerData.inventoryin in the player class is not changing when i try to change it on the inventoryUpdate with the local pointer inventory: inentory[0] = newItem("sword") and it is changing only the local pointer and not the original variable. I thought that if i never defined a new instance (never used new word) it is only a pointer and it will change the original variable. is there any way to do it? defined a pointer correctly?