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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
If matrix $A = \left[ {\begin{array}{*{20}{c}}1&0&{ - 1}\\3&4&5\\0&6&7\end{array}} \right]$ and its inverse is denoted by ${A^{ - 1}} = \left[ {\begin{array}{*{20}{c}}{{a_{11}}}&{{a_{12}}}&{{a_{13}}}\\{{a_{21}}}&{{a_{22}}}&{{a_{23}}}\\{{a_{31}}}&{{a_{32}}}&{{a_{33}}}\end{array}} \right]$, then the value of ${a_{23}}$=
  • A
    $\frac{{21}}{{20}}$
  • B
    $\frac{1}{5}$
  • ✓
    $\frac{2}{5}$
  • D
    $ - \frac{2}{5}$
✓

Answer

Correct option: C.
$\frac{2}{5}$
c
(c) $|A|\, = \, - 20$

$\therefore \,\,{a_{23}} = \frac{{{\rm{Cofactor of 6}}}}{{ - 20}} = \frac{{ - 8}}{{-20}} = \frac{{  2}}{5}$.

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