Given A=(0100)A = \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix}A=(0010), what is eAte^{At}eAt?
(1t01)\begin{pmatrix} 1 & t \\ 0 & 1 \end{pmatrix}(10t1)
(10t1)\begin{pmatrix} 1 & 0 \\ t & 1 \end{pmatrix}(1t01)
(et00et)\begin{pmatrix} e^t & 0 \\ 0 & e^t \end{pmatrix}(et00et)
(1t2/201)\begin{pmatrix} 1 & t^2/2 \\ 0 & 1 \end{pmatrix}(10t2/21)