If A = [ * 20 c 0&1 1&0 ],then A^4 = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}0&1 \\ 1&0\end{array}} \right],$then ${A^4}$=

✓
$\left[ {\begin{array}{*{20}{c}}1&0 \\ 0&1\end{array}} \right]$
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
$\left[ {\begin{array}{*{20}{c}}0&1 \\1&0\end{array}} \right]$

✓

Answer

Correct option: A.

$\left[ {\begin{array}{*{20}{c}}1&0 \\ 0&1\end{array}} \right]$

a
(a) We have $A = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right]$

$\therefore$ ${A^2} = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right]\,\,\left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right] = {I_2}$

$\therefore$ ${A^4} = {A^2}.{A^2} = {I_2}.{I_2} = {I_2} = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$.

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