Answer
37
Work Step by Step
(a) $|A|=\begin{vmatrix}
-7 & -2\\
1 & -5
\end{vmatrix}=(-7)(-5)-(1)(-2)=37$
b) Using elementary row operations:
$|A|=\begin{vmatrix}
-7 & -2\\
1 & -5
\end{vmatrix}=\begin{vmatrix}
6 & 6\\
0 & \frac{-37}{7}
\end{vmatrix}=37$
c) Using the Cofactor Expansion Theorem
$|A|=A_{11}C_{11}+A_{12}C_{12}=(-7)(-5)+(-2)(-1)=37$
