JEE Math Practice Question

The set of all values of $$\mathrm{t\in \mathbb{R}}$$, for which the matrix $$\left[ {\begin{matrix} {{e^t}} & {{e^{ - t}}(\sin t - 2\cos t)} & {{e^{ - t}}( - 2\sin t - \cos t)} \\ {{e^t}} & {{e^{ - t}}(2\sin t + \cos t)} & {{e^{ - t}}(\sin t - 2\cos t)} \\ {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \\ \end{matrix} } \right]$$ is invertible, is :

1. A.$$\left\{ {k\pi ,k \in \mathbb{Z}} \right\}$$
2. B.$$\mathbb{R}$$
3. C.$$\left\{ {(2k + 1){\pi \over 2},k \in \mathbb{Z}} \right\}$$
4. D.$$\left\{ {k\pi + {\pi \over 4},k \in \mathbb{Z}} \right\}$$