The inverse of the matrix [ * 20 c 5& - 2 3&1 ] is - Vidyadip

MCQ

The inverse of the matrix $\left[ {\begin{array}{*{20}{c}}5&{ - 2}\\3&1\end{array}} \right]$ is

✓
$\frac{1}{{11}}\left[ {\begin{array}{*{20}{c}}1&2\\{ - 3}&5\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}1&2\\{ - 3}&5\end{array}} \right]$
C
$\frac{1}{{13}}\left[ {\begin{array}{*{20}{c}}{ - 2}&5\\1&3\end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}}1&3\\{ - 2}&5\end{array}} \right]$

✓

Answer

Correct option: A.

$\frac{1}{{11}}\left[ {\begin{array}{*{20}{c}}1&2\\{ - 3}&5\end{array}} \right]$

a
(a) $A = \left[ {\begin{array}{*{20}{c}}5&{ - 2}\\3&1\end{array}} \right]$

$|A|\, = 11,{A_{11}} = 1,{A_{12}} = - 3,{A_{21}} = 2,{A_{22}} = 5$

${A^{ - 1}} = \frac{1}{{11}}\left[ {\begin{array}{*{20}{c}}1&2\\{ - 3}&5\end{array}} \right]$.

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