Show that – a is the inverse of a for the addition operation '+' on R and `1/a` is the inverse of `a ne 0 `for the multiplication operation X on R.

Explanation

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

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

1. **Definition of Inverse for Addition**: The additive inverse of a number \(a\) is a number \(b\) such that:
\[ a + b = 0 \]
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