A metal M forms an oxide having the formula `M_(2)O_(3)`. It dissolves both in dilute hydrochloric acid and dilute sodium hydroxide solution. Identify the metal and write equations for the reactions involved.

Explanation

To solve the problem, we need to identify the metal \( M \) that forms an oxide with the formula \( M_2O_3 \) and can react with both dilute hydrochloric acid and dilute sodium hydroxide solution.

### Step-by-Step Solution:

1. **Identify the Metal**:
- The oxide formula \( M_2O_3 \) suggests that the metal \( M \) has a valency of +3.
- Metals that typically form oxides with this formula include aluminum (Al), chromium (Cr), and iron (Fe). However, we need to find one that reacts with both acids and bases.

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