\LL\left( \begin{tikzpicture}[baseline]
    \draw(-.5,-.5)-- (.5,.5);
    \draw (-.1,.1) -- (-.5,.5);
    \draw (.1,-.1) -- (.5,-.5);
    \draw (.5,-.5) .. controls (1,-1) and (1,1) .. (.5,.5);
\end{tikzpicture}\right) 
=
a \begin{tikzpicture}[baseline]
    \draw (1.5,.5) .. controls (2,0) .. (1.5,-.5);
\end{tikzpicture}
\text{\quad and \quad}
\LL\left(
\begin{tikzpicture}[baseline,xscale=-1]
    \draw (-.5,-.5)-- (.5,.5);
    \draw (-.1,.1) -- (-.5,.5);
    \draw (.1,-.1) -- (.5,-.5);
    \draw[xscale=-1] (.5,-.5) .. controls (1,-1) and (1,1) .. (.5,.5);
\end{tikzpicture}\right)
=
a^{-1} \begin{tikzpicture}[baseline]
    \draw (1.5,.5) .. controls (2,0) .. (1.5,-.5);
\end{tikzpicture}