Calculate the determinant of the $2\times 2$ matrix $\left[\begin{array}{cc}7& 3\\ 4& 9\end{array}\right]$. Give your answer as an integer.

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 $a=7$, $b=3$, $c=4$, $d=9$ from the given matrix.
3. Compute the product $ad=7\times 9=63$.
4. Compute the product $bc=3\times 4=12$.
5. Subtract: $\det =ad-bc=63-12=51$.
6. State the final value.

Concept tested: Determinant of a 2×2 matrix

Published 8 September 2026 · How this solution was prepared and checked