If A = [ * 20 c i&0 0& - i ],B = [ * 20 c 0&i &0 ], where i = - 1… - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&{ - i}\end{array}} \right],B = \left[ {\begin{array}{*{20}{c}}0&i\\i&0\end{array}} \right]$, where $i = \sqrt { - 1} $, then the correct relation is

A
$A + B = O$
✓
${A^2} = {B^2}$
C
$A - B = O$
D
${A^2} + {B^2} = O$

✓

Answer

Correct option: B.

${A^2} = {B^2}$

b
(b) Relation ${A^2} = {B^2}$is true because ${A^2} = \left[ {\begin{array}{*{20}{c}}{ - 1}&0\\0&{ - 1}\end{array}} \right]$ and ${B^2} = \left[ {\begin{array}{*{20}{c}}{ - 1}&0\\0&{ - 1}\end{array}} \right]$have same matrices.

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