If A=(1001)A = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}A=(1001), what is A100A^{100}A100?
(10000100)\begin{pmatrix} 100 & 0 \\ 0 & 100 \end{pmatrix}(10000100)
(0110)\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}(0110)
(11001001)\begin{pmatrix} 1 & 100 \\ 100 & 1 \end{pmatrix}(11001001)
(1001)\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}(1001)