Inverse element

The inverse element is the opposite of a number or equation. The inverses of formula_1 in addition is formula_2 (called the additive inverse), and formula_3 or formula_4 in multiplication (called the multiplicative inverse, or reciprocal).
In general, given an element "g" in a group "S" equipped with an operation formula_5, an inverse element of "g" is an element "g*" such that formula_6 and formula_7 are both equal to the identity element (of the group). Other examples of inverse include inverse function and matrix inverse.