the solution, when added to the solution (A), gives a reddish brown precipitate
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Solution
Reaction as per the question is given below:
Ferric chloride reacts with Sodium hydroxide undergoes a double decomposition reaction to gives an insoluble compound in the form of a reddish brown precipitate of Ferric hydroxide and another soluble compound Sodium chloride as products.
The reaction in which radicals are exchanged in their solution state is known as the double decomposition (double displacement) reaction.
Thus, the solution (A) which is added is Sodium hydroxide.