If $A=\begin{bmatrix} e^{t} & e^{-t}\cos t & e^{-t}\sin t\\[4pt] e^{t} & -e^{-t}\cos t - e^{-t}\sin t & -e^{-t}\sin t + e^{-t}\cos t\\[4pt] e^{t} & 2e^{-t}\sin t & -2e^{-t}\cos t \end{bmatrix}$, then $A$ is: