Consider the matrix A=(1a01)A = \begin{pmatrix} 1 & a \\ 0 & 1 \end{pmatrix}A=(10a1). Compute A100A^{100}A100.
(1100a01)\begin{pmatrix} 1 & 100a \\ 0 & 1 \end{pmatrix}(10100a1)
(1a10001)\begin{pmatrix} 1 & a^{100} \\ 0 & 1 \end{pmatrix}(10a1001)
(110001)\begin{pmatrix} 1 & 100 \\ 0 & 1 \end{pmatrix}(101001)
(11000a100)\begin{pmatrix} 1 & 100 \\ 0 & a^{100} \end{pmatrix}(10100a100)