Chapter 9.3, Problem 17E

In Problems 17-20, find the matrix $X^{-1}\left(t\right)$ whose value at $\text{t}$ is the inverse of the given matrix $X\left(t\right)$.

$X\left(t\right)=\left[\begin{array}{cc}{e}^t& e^{4t}\\ e^t& 4e^{4t}\end{array}\right]$