Answer
False
Work Step by Step
Let $A=\begin{bmatrix}
0 & 2e^t& 0\\5e^t&0 &0\\0&0&0
\end{bmatrix}$
We know $\frac{dA}{dt}=A$ but for $ce^tI_n$, $A$ will be $A=\begin{bmatrix}
ce^t & 0 & 0\\0& ce^t &0\\0&0& ce^t
\end{bmatrix}$
Hence, the statement is false.