If A = ( * 20 c i&1 0&i ), then A^4 equals - Vidyadip

MCQ

If $A = \left( {\begin{array}{*{20}{c}}i&1\\0&i\end{array}} \right)$, then ${A^4}$ equals

✓
$\left( {\begin{array}{*{20}{c}}1&{ - 4i}\\0&1\end{array}} \right)$
B
$\left( {\begin{array}{*{20}{c}}{ - 1}&{ - 4i}\\0&{ - 1}\end{array}} \right)$
C
$\left( {\begin{array}{*{20}{c}}{ - i}&4\\0&i\end{array}} \right)$
D
$\left( {\begin{array}{*{20}{c}}1&4\\0&1\end{array}} \right)$

✓

Answer

Correct option: A.

$\left( {\begin{array}{*{20}{c}}1&{ - 4i}\\0&1\end{array}} \right)$

a
(a) $A.A = \left[ {\begin{array}{*{20}{c}}{ - 1}&{2i}\\0&{ - 1}\end{array}} \right]$ ,

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

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