Q.Evaluate the determinant $\begin{vmatrix}-5&3\\4&-2\end{vmatrix}$.

Careful sign handling with two negative entries is the main thing to get right here.

$(-5)(-2)-3(4)=10-12=-2$.

Check (independent recomputation): computing $(-5)\times(-2)$ on its own confirms it equals $+10$ (a negative times a negative), and $3\times4=12$ is straightforward, so $10-12=-2$ is confirmed.

Miscalculating $(-5)(-2)$ as $-10$ instead of $+10$, which would wrongly give a determinant of $-10-12=-22$.