JEE Main 20199 Jan, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002If A=[ete−tcoste−tsintet−e−tcost−e−tsint−e−tsint+e−tcostet2e−tsint−2e−tcost]A = \left[ {\matrix{ {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr {{e^t}} & { - {e^{ - t}}\cos t - {e^{ - t}}\sin t} & { - {e^{ - t}}\sin t + {e^{ - t}}co{\mathop{\rm s}\nolimits} t} \cr {{e^t}} & {2{e^{ - t}}\sin t} & { - 2{e^{ - t}}\cos t} \cr } } \right]A=etetete−tcost−e−tcost−e−tsint2e−tsinte−tsint−e−tsint+e−tcost−2e−tcost then A is :AOption A. invertible for all t∈\in∈R.BOption B. invertible only if t === π\piπCOption C. not invertible for any t∈\in∈RDOption D. invertible only if t === π2{\pi \over 2}2π.CheckSkip · show solution
