If A = [ * 20 c i&0 0&i ], then A^2 = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&i\end{array}} \right]$, then ${A^2} = $

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

✓

Answer

Correct option: B.

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

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

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

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