Q.Evaluate the determinant of $A=\begin{pmatrix}4&3\\2&5\end{pmatrix}$.

A 2×2 determinant is the product of the leading diagonal minus the product of the other diagonal.

$|A|=4(5)-3(2)=20-6=14$.

Check (independent recomputation): recomputing the two products separately — leading diagonal product $4\times5=20$, other diagonal product $3\times2=6$, difference $20-6=14$ — matches exactly.

Computing $ad-bc$ with the wrong pairing, e.g. $4(2)-3(5)$ (multiplying same-row entries together) instead of the correct diagonal products $4(5)$ and $3(2)$.