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3 and 4 .Determinants and Matrices
easy
જો $A = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right],$ તો ${A^4}$=
A
$\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}1&1\\0&0\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}0&0\\1&1\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right]$
Solution
(a) We have $A = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right]$
$\therefore$ ${A^2} = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right]\,\,\left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right] = {I_2}$
$\therefore$ ${A^4} = {A^2}.{A^2} = {I_2}.{I_2} = {I_2} = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$.
Standard 12
Mathematics
