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

If $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 3 & 4 \\ 3 & 4 & 3\end{array}\right]$, then $A^{-1}=$
  1. $-\frac{1}{4}\left[\begin{array}{ccc}-7 & -6 & -1 \\ 9 & 6 & -1 \\ -5 & -2 & 1\end{array}\right]$
  2. $\frac{1}{4}\left[\begin{array}{ccc}-7 & 6 & -1 \\ 9 & -6 & -1 \\ -5 & 2 & 1\end{array}\right]$
  3. $-\frac{1}{4}\left[\begin{array}{ccc}-7 & 6 & 1 \\ 9 & -1 & 1 \\ -5 & 2 & 1\end{array}\right]$
  4. $-\frac{1}{4}\left[\begin{array}{ccc}-7 & 6 & -1 \\ 9 & -6 & -1 \\ -5 & 2 & 1\end{array}\right]$

Solution

$\because A^{-1}=\frac{\operatorname{adj}(A)}{|A|}=-\frac{1}{4}\left[\begin{array}{ccc}-7 & 6 & -1 \\ 9 & -6 & -1 \\ -5 & 2 & 1\end{array}\right]$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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