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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
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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