Would you be able to check if water is hard by using a detergent?

Explanation

Detergents are generally sodium salts of sulphonic acids or ammonium salts with chlorides or bromides ions ,etc . Unlike soap ,they do not react with calcium and magnesium ions present in hard water to form scum .They given a good amount of lather irrespective of whether the water is hard or soft .This means thta detergent can be used in both soft and hard water .Therefore ,it cannot be used to check whether the water is hard or not.