What is $A$ if

$e^{At}=\left[\begin{array}{cc}2e^{-2t}-e^{-3t}& e^{-2t}-e^{-3t}\\ 2e^{-3t}-2e^{-2t}& 2e^{-3t}-e^{-2t}\end{array}\right]$

HINT: What is the derivative of $e^{At}?$