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: $Av_{i}=\lambda _{i}v_{i}\,$, we have:

$AT=A(v_{1}|v_{2}|\cdots |v_{n})=(Av_{1}|Av_{2}|\cdots |Av_{n})=(\lambda _{1}v_{1}|\lambda _{2}v_{2}|\cdots |\lambda _{n}v_{n})\,$ $=(v_{1}|v_{2}|\cdots |v_{n}){\begin{pmatrix}\lambda _{1}\\&\lambda _{2}\\&&\ddots \\&&&\lambda _{n}\end{pmatrix}}=T\Lambda \,$

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

--Shuo