If matrix A = [ * 20 c 1&0& - 1 3&4&5 0&6&7 ] and its inverse is … - Vidyadip

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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