If A = [ * 20 c 2&3 4&6 ], then A^ - 1 = - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}2&3\\4&6\end{array}} \right]$, then ${A^{ - 1}}$=

A
$\left[ {\begin{array}{*{20}{c}}1&2\\{ - 3/2}&3\end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}}2&{ - 3}\\4&6\end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}}{ - 2}&4\\{ - 3}&6\end{array}} \right]$
✓
Does not exist

✓

Answer

Correct option: D.

Does not exist

d
(d) Given,$A = \left[ {\begin{array}{*{20}{c}}2&3\\4&6\end{array}} \right]$,

we know that ${A^{ - 1}} = \frac{{adj.A}}{{|A|}}$.

Therefore, $|A|\,\, = \,\,[12 - 12] = 0.$

Since $|A|$ is zero,

therefore inverse of $A$ does not exist.

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