Answer
See solution
Work Step by Step
We first need to convert matrix A into a triangular form U through row reduction.
$U=\begin{bmatrix}
a&b\\
0&d-bc/a
\end{bmatrix}$. The determinant is $a(d-bc/a)=ad-bc$
If a=0, we need to switch the rows.
$U=\begin{bmatrix}
c&d\\
0&b
\end{bmatrix}$. The determinant is $-cb$, with a negative sign because we interchanged two rows and without the ad term because a is 0.
