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  4. If A=[1 -1 2 2 3 1 1 -2 3] then textadj(A-1)=

Q. If $A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}$ then $\text{adj}\left(A^{-1}\right)=$

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Solution:

$\text{adj}\left(A^{-1}\right)=(\text{adj} A)^{-1}=\frac{A}{|A|}$ Now,
$|A|=1 .(9+2)+1 \cdot(6-1)+2 \cdot(-4-3)$
$=11+5-14=2 $
$\therefore(\text{adj} A)^{-1}=\frac{1}{2} A$

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