Chapter 11.3, Problem 58E

To determine

To find:

The inverse of the given matrix $\left[\begin{array}{cc}{e}^x& -e^{2x}\\ e^{2x}& e^{3x}\end{array}\right]$ and the value(s) of $x$ the such that inverse of $\left[\begin{array}{cc}{e}^x& -e^{2x}\\ e^{2x}& e^{3x}\end{array}\right]$ does not exist.