Step 1: Understanding the reaction.
When magnesium nitride (Mg\(_3\)N\(_2\)) reacts with water, it produces magnesium hydroxide (Mg(OH)\(_2\)) and ammonia gas (NH\(_3\)) as products. The balanced chemical equation is:
\[
\text{Mg}_3\text{N}_2 + 6\text{H}_2\text{O} \rightarrow 3\text{Mg(OH)}_2 + 2\text{NH}_3
\]
Step 2: Analyzing the options. (A) Mg(OH)\(_2\) and NH\(_3\): Correct. This is the correct product of the reaction. (B) Mg(OH)\(_2\) and N\(_2\)O: Incorrect. N\(_2\)O is not produced in this reaction. (C) MgO and NH\(_3\): Incorrect. Magnesium oxide (MgO) is not a product of this reaction. (D) MgO and NH\(_4\)OH: Incorrect. Magnesium hydroxide (Mg(OH)\(_2\)) and ammonia (NH\(_3\)) are the correct products. Step 3: Conclusion.
The correct answer is (A) Mg(OH)\(_2\) and NH\(_3\).