A) 27 A
B) 81 A
C) 243 A
D) 729 A
E) 3 A
Correct Answer: D
Solution :
Given, \[A=\left[ \begin{matrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \\ \end{matrix} \right]\] \[\therefore \] \[A=3\left| \begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right|\] \[\therefore \] \[{{A}^{2}}=3\left[ \begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right].3\left[ \begin{matrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{matrix} \right]\] \[=9\left[ \begin{matrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \\ \end{matrix} \right]=9A\] \[\therefore \] \[{{A}^{4}}={{A}^{2}}.{{A}^{2}}\] \[=9A.9A=81{{A}^{2}}=81.9A\] \[=729A\]
You need to login to perform this action.
You will be redirected in
3 sec
