If A = [ * 20 c 0&1 0&0 ]and AB = O, then B = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}0&1\\0&0\end{array}} \right]$and $AB = O$, then $B =$

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

✓

Answer

Correct option: D.

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

d
(d) Since $\left[ {\begin{array}{*{20}{c}}0&1\\0&0\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}{ - 1}&0\\0&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0&0\\0&0\end{array}} \right] = O = AB$
==> $B = \left[ {\begin{array}{*{20}{c}}{ - 1}&0\\0&0\end{array}} \right]$.

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