If A = [ * 20 c 3&2 1&4 ], then A(adj ,A) = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}3&2\\1&4\end{array}} \right]$, then $A(adj\,A) = $

✓
$\left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}0&{10}\\{10}&0\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}{10}&1\\1&{10}\end{array}} \right]$
D
None of these

✓

Answer

Correct option: A.

$\left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$

a
(a) $A(adj\,A) = \left[ {\begin{array}{*{20}{c}}3&2\\1&4\end{array}} \right]\,.\,\left[ {\begin{array}{*{20}{c}}4&{ - 2}\\{ - 1}&3\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$.

Aliter : $A\,(adj\,A) = |A|I = 10{\rm{ }}\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$.

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