Question

\text { Consider the following matrix: } A=\left(\begin{array}{cc} e^{x} & e^{-x} \\ e^{x} & 2 e^{x} \end{array}\right) Find the condition for the inverse matrix to exit. Simplify your answer completely

(i.e. if it is a log, use the log properties to write your final \text { answer as } \pm \log _{a}\left(b^{n}\right) Hint: Recall that an inverse has no inverse, if its determinant is zero. (Evaluate the determinant of A, equate it to zero and exclude that bad point if any).

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