$\begin{equation}
\begin{aligned}
(E'A')^{\tau} &= ((M^{\tau}M)(M^{-1}AM))^{\tau} = (M^{\tau}AM)^{\tau} \\
&= M^{\tau}A^{\tau}(M^{\tau})^{\tau} = M^{\tau}AM = M^{\tau}M(M^{-1}AM) \\
&= E'A'
\end{aligned}
\end{equation}$