Question

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

• A. $\frac{1}{7}\left[\begin{array}{cc}-1& -2\\ 4& 1\end{array}\right]$
• B. $\frac{1}{7}\left[\begin{array}{cc}1& 2\\ -4& -1\end{array}\right]$
• C. $\frac{1}{7}\left[\begin{array}{cc}-1& 2\\ 4& -1\end{array}\right]$
• D. Does not exist

Answer 1

Answer: (A)

$|A|=-1+8=7$
$\text{adj}\left(A\right)=\left[\begin{array}{cc}+\left(-1\right)& -\left(2\right)\\ -\left(-4\right)& +\left(1\right)\end{array}\right]=\left[\begin{array}{cc}-1& -2\\ 4& 1\end{array}\right]$
$\because A^{-1}=\frac{1}{|A|}\text{Adj}A$
$A^{-1}=\frac{1}{7}\left[\begin{array}{cc}-1& -2\\ 4& 1\end{array}\right]$