If A = [ * 20 c 1&0 2&0 ],B = [ * 20 c 0&0 1& 12 ], then - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}1&0\\2&0\end{array}} \right],B = \left[ {\begin{array}{*{20}{c}}0&0\\1&{12}\end{array}} \right]$, then

A
$AB = O,BA = O$
✓
$AB = O,BA \ne O$
C
$AB \ne O,BA = O$
D
$AB \ne O,BA \ne O$

✓

Answer

Correct option: B.

$AB = O,BA \ne O$

b
(b) $AB = \,\left[ {\begin{array}{*{20}{c}}1&0\\2&0\end{array}\,} \right]\,\left[ {\begin{array}{*{20}{c}}0&0\\1&{12}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0&0\\0&0\end{array}} \right] = O$

while $BA = \left[ {\begin{array}{*{20}{c}}0&0\\1&{12}\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&0\\2&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0&0\\{25}&0\end{array}} \right]\, \ne O$.

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