This Demonstration shows an example of an improper involution
, that is,
does not imply
be a commutative ring different from
is the ring of all 2×2 matrices over
, then the involution
is improper. Specifically, for
, even if
A *-ring (or involutive ring, or ring with involution) is a ring with an involution
The example based on matrix inversion is taken from [1, p. 11]. For definitions, see [1, p. 3, p. 10].
 S. K. Berberian, Baer *-Rings
, New York: Springer-Verlag, 1972.