JEE Math Practice Question

If $$A = \left[ {\begin{matrix} {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \\ {{e^t}} & { - {e^{ - t}}\cos t - {e^{ - t}}\sin t} & { - {e^{ - t}}\sin t + {e^{ - t}}co{\mathop{\rm s}\nolimits} t} \\ {{e^t}} & {2{e^{ - t}}\sin t} & { - 2{e^{ - t}}\cos t} \\ \end{matrix} } \right]$$ then A is :

1. A.invertible for all t$$ \in $$R.
2. B.invertible only if t $$=$$ $$\pi $$
3. C.not invertible for any t$$ \in $$R
4. D.invertible only if t $$=$$ $${\pi \over 2}$$.