Answer
See below
Work Step by Step
Given: $A=\begin{bmatrix}
-3& 0\\
0 & 5
\end{bmatrix}$
We can see $A$ is diagonal, then $e^{At}=diag(e^{-3},e^t)=\begin{bmatrix}
e^{-3}& 0\\
0 & e^5
\end{bmatrix}$
For all $n \times n$ matrices A, $e^{At}$ is invertible and
$$e^{-At}=)e^{At})^{-1}\\
e^{-At}=\frac{1}{e^2}\begin{bmatrix}
e^5 & 0\\
0 & e^{-3}
\end{bmatrix}=\begin{bmatrix}
e^3 & 0\\
0 & e^{-5}
\end{bmatrix}$$
