# How do you find the determinant of ((7, -1), (6, -2))?

Feb 13, 2016

$- 8$

#### Explanation:

The determinant of the $2 \times 2$ matrix

$\left(\begin{matrix}a & b \\ c & d\end{matrix}\right)$

is equal to $\textcolor{red}{a d - b c}$.

Here, with the matrix

$\left(\begin{matrix}7 & - 1 \\ 6 & - 2\end{matrix}\right)$

we see that

$\left\{\begin{matrix}a = 7 \\ b = - 1 \\ c = 6 \\ d = - 2\end{matrix}\right.$

Thus, the determinant of the matrix is equal to

$a d - b c = \left(7\right) \left(- 2\right) - \left(- 1\right) \left(6\right) = - 14 + 6 = \textcolor{b l u e}{- 8}$