Show that a is the inverse of a for the addition operation + on R and `1/a`is the inverse of `a!=0`for the multiplication operation `xx` on R.

Explanation

To show that \( -a \) is the inverse of \( a \) for the addition operation \( + \) on \( \mathbb{R} \) and \( \frac{1}{a} \) is the inverse of \( a \) (where \( a \neq 0 \)) for the multiplication operation \( \cdot \) on \( \mathbb{R} \), we will follow these steps:

### Step 1: Proving that \( -a \) is the inverse of \( a \) for addition

1. **Definition of Inverse for Addition**: An element \( b \) is the inverse of \( a \) under addition if:
\[ a + b = 0 \quad \text{and} \quad b + a = 0 \]
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