If A=(1000)A = \begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}A=(1000), what is the value of AkA^kAk for any positive integer kkk?
(1000)\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}(1000)
(1001)\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}(1001)
(k000)\begin{pmatrix} k & 0 \\ 0 & 0 \end{pmatrix}(k000)
(0000)\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}(0000)