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

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

Related facts

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