Definition: The Inverse Property

The inverse property refers to the relationship between two elements under a specific operation, where one undoes the effect of the other.

There are two main types of inverse properties: additive inverse and multiplicative inverse.

Explanation:

The Additive Inverse Property states that any element 'a' in a mathematical system has an additive inverse '- a', and when added together, they result in an additive identity element '0'. Symbolically, it can be expressed as a: a + (- a) = 0.

The Multiplicative Inverse Property states that any non-zero element has a reciprocal or multiplicative inverse denoted as \$ a^-1\$. When a non-zero element is multiplied by its reciprocal \$ a^-1 \$, the result is always 1.

Symbolically, it can be expressed as:\$a \times (a^-1) = 1 \$.