# Inverse10

Right multiplication by the inverse is a left group action of a group on itself
Counterexamples regarding one-sided zero divisors and inverses
Basic properties of left and right units and left and right zero divisors
Additive subgroups of the rationals which are closed under inversion are trivial
The inversion map is a homomorphism precisely on abelian groups
Every group element of odd order is an odd power of its square
A group element and its inverse have the same order
Laws of exponents in a group
Basic property of inverses of group elements of finite order
The inverse of a product is the reversed product of inverses