A) \[\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} -1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\]
Correct Answer: D
Solution :
Given, Matrix\[A=\,\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\]. We know that \[{{A}^{2}}=A.A=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\,\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]=\left[ \begin{matrix} -1 & 0 \\ 0 & -1 \\ \end{matrix} \right].\] Therefore \[{{A}^{16}}={{({{A}^{2}})}^{8}}={{\left[ \begin{matrix} -1 & 0 \\ 0 & -1 \\ \end{matrix} \right]}^{8}}=\left[ \begin{matrix} {{(-1)}^{8}} & 0 \\ 0 & {{(-1)}^{8}} \\ \end{matrix} \right]\]\[=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\].
You need to login to perform this action.
You will be redirected in
3 sec
