Answer
See answers below
Work Step by Step
a) We have $det(A)=a_{11}C_{11}+a_{21}C_{21}$
with $C_{11}=(-1)^{1+1}.(-6)=-6$
$C_{12}=(-1)^{1+2}.(-15)=15$
$\det(A)=a_{11}C_{11}+a_{12}C_{12}=(-6).5+15.2=0$
b) $C_{21}=(-1)^{2+1}.2=-2$
$C_{22}=(-1)^{2+2}.5=5$
then $M_C=\begin{bmatrix}
C_{11} & C_{12}\\
C_{21} & C_{21}
\end{bmatrix}=\begin{bmatrix}
-6 &15\\
-2 &5
\end{bmatrix}$
c) $adj(A)=\begin{bmatrix}
-6& -2\\
15& 5
\end{bmatrix}$
d) Because $\det(A)=0 $, we are not able to find $A^{-1}$
