A name for this property? Let $*$ be an operation such that $(xy)^* = y^*x^*$, e.g. if $x,y$ are $2\times2$ matrices and $*$ is "take the inverse" or if $x,y$ are operators and if $*$ is the adjoint.
Is there a name for such a property ?

In noncommutative ring theory (which might be applied to real matrices), a map $\phi:R\to R$ such that $\phi(ab)=\phi(b)\phi(a)$ and $\phi(a+b)=\phi(a)+\phi(b)$ may be called a ring-homomorphism $R\to R^{\operatorname{op}}$.
What's $R^{\operatorname{op}}$? Basically if $(R,+,\cdot)$ is a ring, $R^{\operatorname{op}}$ is the ring $(R,+,\cdot^{\operatorname{op}})$ given by $a\cdot^{\operatorname{op}}b:=b\cdot a$, while the sum remains the same.
