Transpose-inverse map induces inner automorphism on projective general linear group of degree two
From Groupprops
Statement
Suppose is any commutative unital ring. Let
be the General linear group (?) of degree two over
,
be the center of
(which is also the group of scalar matrices, because Center of general linear group is group of scalar matrices over center), and let
be the Projective general linear group (?) of degree two over
.
Then, the automorphism of induced by the Transpose-inverse map (?) automorphism of
is an inner automorphism of
.