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 Projective general linear group (?). Then, $G$ is a 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