I keep getting mixed up on whether the diagonalized form of A is T^(-1)AT or TAT^(-1). Is there an easy way to remember the correct form?

This is the way I use to remember which form to use. Note the $T$ matrix consists of all the eigenvectors, $v_i$, of $A$: $T=(v_1|v_2|\cdots |v_n)$. Using the definition of (right) eigenvectors: $A{v}_i={\lambda }_i{v}_i$, we have:

$AT=A(v_1|v_2|\cdots |v_n)=(A{v}_1|A{v}_2|\cdots |A{v}_n)=({\lambda }_1{v}_1|{\lambda }_2{v}_2|\cdots |{\lambda }_n{v}_n)$ $=(v_1|v_2|\cdots |v_n)\left(\begin{array}{c}{\lambda }_1\\ & {\lambda }_2\\ & & \ddots \\ & & & {\lambda }_n\end{array}\right)=T\mathrm{\Lambda }$

Right multiply each side by $T^{-1}$: $A=T\mathrm{\Lambda }{T}^{-1}$, which is the correct form.

--Shuo