Solve the following equations

Question:

If $A=\left[\begin{array}{cc}3 & 1 \\ 2 & -3\end{array}\right]$, then find |adj $A \mid$.

Solution:

$|A|=\left|\begin{array}{cc}3 & 1 \\ 2 & -3\end{array}\right|=-11$

$\therefore|\operatorname{adj} A|=|A|^{n-1}=(-11)^{2-1}=-11$

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