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?

From MurrayWiki

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:

$AT = A(v_1|v_2|\cdots|v_n) = (Av_1|Av_2|\cdots|Av_n) = (\lambda_1v_1|\lambda_2v_2|\cdots|\lambda_nv_n) \,$ $= (v_1|v_2|\cdots|v_n)\begin{pmatrix} \lambda_1 \\ & \lambda_2 \\ & & \ddots \\ & & & \lambda_n \end{pmatrix}=T\Lambda \,$