why doesn't the element get swapped

public static void SwapArray(ref int[,] arr)
    {
        for (int i = 0; i < arr.GetLength(0); i++)
        {
            for (int j = 0; j < arr.GetLength(0); j++)
            {
                int temp = arr[i, j];
                arr[i, j] = arr[j, i];
                arr[j, i] = temp;
                Console.Write(arr[i, j] + " ");
            }
            Console.WriteLine();
        }
    }

even if the parameter is without a ref modifier the array doesn't change. a copy of the reference is passed as a parameter right?