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 General linear group (?). Then, $G$ is a 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. Transpose-inverse map is class-inverting automorphism for general linear group
2. Class-inverting automorphism implies every element is automorphic to its inverse

Proof

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