1.Let A=(111011001)A = \begin{pmatrix}1&1&1\\0&1&1\\0&0&1\end{pmatrix}A=100110111. For positive integer nnn, AnA^nAn isa.(1nn20n2n00n)\begin{pmatrix}1&n&n^2\\0&n^2&n\\0&0&n\end{pmatrix}100nn20n2nnb.(1nn(n+1)201n001)\begin{pmatrix}1&n&\frac{n(n+1)}{2}\\0&1&n\\0&0&1\end{pmatrix}100n102n(n+1)n1c.(1n2n0nn200n2)\begin{pmatrix}1&n^2&n\\0&n&n^2\\0&0&n^2\end{pmatrix}100n2n0nn2n2d.(1n2n−10n+12n200n+12)\begin{pmatrix}1&n&2n-1\\0&\frac{n+1}{2}&n^2\\0&0&\frac{n+1}{2}\end{pmatrix}100n2n+102n−1n22n+1Login to continueOnly logged in users canattempt or see the solution.
