Inverse element

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

In general, given an element g in a group S equipped with an operation $\circ$, an inverse element of g is an element g* such that $g\circ g^{*}$ and $g^{*}\circ g$ 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)