Inverse element

The inverse element is the opposite of a number or equation. The inverses of [math]\displaystyle{ x }[/math] in addition is [math]\displaystyle{ -x }[/math] (called the additive inverse), and [math]\displaystyle{ \tfrac{1}{x} }[/math] or [math]\displaystyle{ x^{-1} }[/math] in multiplication (called the multiplicative inverse, or reciprocal).

In general, given an element g in a group S equipped with an operation [math]\displaystyle{ \circ }[/math], an inverse element of g is an element g* such that [math]\displaystyle{ g \circ g^* }[/math] and [math]\displaystyle{ g^* \circ g }[/math] are both equal to the identity element (of the group). Other examples of inverse include inverse function and matrix inverse.

Related pages

• Field (mathematics), a set equipped with additive inverses and multiplicative inverses (except for zero)