Find the determinant of the matrix $A=\left(\begin{array}{cc}5& 2\\ 3& -4\end{array}\right)$.

Step-by-step solution

1. Write the formula for a $2\times 2$ determinant: $\det \left(\begin{array}{cc}a& b\\ c& d\end{array}\right)=ad-bc$.
2. Identify $a=5$, $b=2$, $c=3$, $d=-4$ from the given matrix.
3. Compute $ad=5\times (-4)=-20$ and $bc=2\times 3=6$.
4. Subtract: $\det A=-20-6=-26$.

Concept tested: Determinant of a $2\times2$ matrix

Published 15 September 2026 · How this solution was prepared and checked