Inverse Elements

Inverse Elements exist for Addition and Multiplication.

For Addition, for every element a the inverse is (-a). Note that a could be -3 and if so then (-a) = +3.

$a + (-a) = 0$

For Multiplication, for every element a the inverse is 1/a. Note that a could be 1/2 and if so then 1/a = 2.

$a * \frac {1} {a} = 1$

As a generalization, we could write the following:

$a * a^{-1} = e$

where ‘e’ is the symbol for the identity element.