I know we have the parity operator for inversion in quantum mechanics and for rotations we have the exponentials of the angular momentum/spin operators. But what if I want to write the operator that represent a reflection for example just switching y to -y, the matrix in real space being:

$$\begin{pmatrix}

1 & 0 & 0\\

0 & -1 & 0\\

0 & 0 & 1

\end{pmatrix}=

\begin{pmatrix}

-1 & 0 & 0\\

0 & -1 & 0\\

0 & 0 & -1

\end{pmatrix}

\begin{pmatrix}

-1 & 0 & 0\\

0 & 1 & 0\\

0 & 0 & -1

\end{pmatrix}

$$ ?

Is it possible to write it as a composition of rotations and/or parity operators? Or is there already an operator for this kind of transformation like partial parity... ? I could not find it on the internet or book chapters.

Thank you for any hints about that.