Answer
Both sides are the same.
Work Step by Step
The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$
where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$
Considering the left side, we have:
$det=wz-xy$
Now, considering the right side we have
$det=w(z+cy)-y(x+cw)=wz+wcy-yx-ycw=wz-xy$
