Q.Evaluate $\begin{vmatrix}6&-2\\-3&4\end{vmatrix}$.

Careful sign-handling is essential when the matrix itself contains negative entries.

$6(4)-(-2)(-3)=24-6=18$.

Note that $(-2)\times(-3)=+6$ (a negative times a negative is positive), so the determinant is $24-6$, not $24+6$.

Check (independent recomputation): recomputing $(-2)(-3)$ on its own confirms it equals $+6$ (not $-6$), and $6(4)=24$ is unaffected by any sign issue — so $24-6=18$ is confirmed correct.

Mishandling the sign of the product of two negative numbers, e.g. computing $(-2)(-3)$ as $-6$ instead of $+6$, which would wrongly give a determinant of $24-(-6)=30$.