If $A=\left[\begin{array}{rr}-2 & 6 \\ -5 & -1\end{array}\right]$ then $A^{-1}$ is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) - $\frac{1}{32}\left[\begin{array}{rr}-1 & -6 \\ 5 & -2\end{array}\right]$
$A=\left[\begin{array}{rr}-2 & 6 \\ -5 & -1\end{array}\right]$
$C_{11}=-1,C_{12}=5$
$C_{21}=-6,C_{22}=-2$
$Adj\,A=\begin{bmatrix}-1&5\\-6&-2\end{bmatrix}^T=\begin{bmatrix}-1&-6\\5&-2\end{bmatrix}$
$|A|=2+30=32$
$A^{-1}=\frac{1}{|A|}Adj\,A=\frac{1}{32}\left[\begin{array}{rr}-1 & -6 \\ 5 & -2\end{array}\right]$