• # question_answer If  $A=\left[ \begin{matrix} 0 & a \\ 0 & 0 \\ \end{matrix} \right],$ find ${{A}^{16}}.$

Given$A=\left[ \begin{matrix} 0 \\ 0 \\ \end{matrix}\,\,\,\begin{matrix} a \\ 0 \\ \end{matrix} \right]$, then ${{A}^{2}}=\left[ \begin{matrix} 0 \\ 0 \\ \end{matrix}\,\,\,\begin{matrix} a \\ 0 \\ \end{matrix} \right]\left[ \begin{matrix} 0 \\ 0 \\ \end{matrix}\,\,\,\begin{matrix} a \\ 0 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 \\ 0 \\ \end{matrix}\,\,\,\begin{matrix} 0 \\ 0 \\ \end{matrix} \right]=O$ $\Rightarrow$   ${{A}^{2}}={{({{A}^{2}})}^{8}}=O$

You need to login to perform this action.
You will be redirected in 3 sec