If P = ( * 20 c i&0& - i 0& - i &i - i &i&0 ) and Q = ( * 20 c - … - Vidyadip

MCQ

If $P = \left( {\begin{array}{*{20}{c}}i&0&{ - i}\\0&{ - i}&i\\{ - i}&i&0\end{array}} \right)$ and $Q = \left( {\begin{array}{*{20}{c}}{ - i}&i\\0&0\\i&{ - i}\end{array}} \right)$,then $PQ$ is equal to

A
$\left( {\begin{array}{*{20}{c}}{ - 2}&2\\1&{ - 1}\\1&{ - 1}\end{array}} \right)$
✓
$\left( {\begin{array}{*{20}{c}}{\,2}&{ - 2}\\{ - 1}&{\,\,\,1}\\{ - 1}&{\,\,\,1}\end{array}} \right)$
C
$\left( {\begin{array}{*{20}{c}}2&{ - 2}\\{ - 1}&{\,\,1}\end{array}} \right)$
D
$\left( {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right)$

✓

Answer

Correct option: B.

$\left( {\begin{array}{*{20}{c}}{\,2}&{ - 2}\\{ - 1}&{\,\,\,1}\\{ - 1}&{\,\,\,1}\end{array}} \right)$

b
(b) First note that $PQ$ must be of order $3 × 2$ and its $(1, 1)$th entry is $i( - i) + 0 - i(i) = 2$.

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