Compute the determinant of the $2\times 2$ matrix $\left[\begin{array}{cc}8& 5\\ 7& 6\end{array}\right]$.

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 $a=8$, $b=5$, $c=7$, $d=6$ from the given matrix.
3. Calculate the product of the main diagonal: $a\times d=8\times 6=48$.
4. Calculate the product of the other diagonal: $b\times c=5\times 7=35$.
5. Subtract the second product from the first: $48-35=13$.
6. Therefore, the determinant equals $13$.

Concept tested: Determinant of a 2×2 matrix

Published 13 September 2026 · How this solution was prepared and checked