Given A=(1101)A = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}A=(1011), what is A100A^{100}A100?
(110001)\begin{pmatrix} 1 & 100 \\ 0 & 1 \end{pmatrix}(101001)
(11000001)\begin{pmatrix} 1 & 10000 \\ 0 & 1 \end{pmatrix}(10100001)
(1101)\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}(1011)
(1001000100)\begin{pmatrix} 100 & 100 \\ 0 & 100 \end{pmatrix}(1000100100)