General linear group implies every element is automorphic to its inverse

Statement
Suppose $$k$$ is a field and $$n$$ is a natural number. Let $$G = GL(n,k)$$ be the fact about::general linear group. Then, $$G$$ is a fact about::group in which every element is automorphic to its inverse.

Related facts

 * Projective general linear group implies every element is automorphic to its inverse
 * Special linear group implies every element is automorphic to its inverse
 * Projective special linear group implies every element is automorphic to its inverse

Facts used

 * 1) uses::Transpose-inverse map is class-inverting automorphism for general linear group
 * 2) uses::Class-inverting automorphism implies every element is automorphic to its inverse

Proof
The proof follows directly from facts (1) and (2).