Find the determinant of the $2\times 2$ matrix $\left[\begin{array}{cc}12& 5\\ 7& 9\end{array}\right]$.

Step-by-step solution

1. Write the determinant formula for a $2\times 2$ matrix: $\det \left[\begin{array}{cc}a& b\\ c& d\end{array}\right]=ad-bc$.
2. Identify $a=12$, $b=5$, $c=7$, $d=9$.
3. Compute $ad=12\times 9=108$.
4. Compute $bc=5\times 7=35$.
5. Subtract: $108-35=73$. Wait, check arithmetic: $12\times 9=108$, $5\times 7=35$, $108-35=73$.
6. Thus the determinant is $73$.

Concept tested: Determinant of $2\times2$ matrix

Published 11 September 2026 · How this solution was prepared and checked