# How do you find the determinant of |(-6,5),(0,-8)|?

##### 1 Answer
Dec 13, 2016

$\left\mid \begin{matrix}- 6 & 5 \\ 0 & - 8\end{matrix} \right\mid = 48$

#### Explanation:

The determinant of a $2 \times 2$ square matrix is given by the formula:

$\left\mid \begin{matrix}a & b \\ c & d\end{matrix} \right\mid = a d - b c$

So in our example:

$\left\mid \begin{matrix}- 6 & 5 \\ 0 & - 8\end{matrix} \right\mid = \left(- 6\right) \left(- 8\right) - \left(5\right) \left(0\right) = 48 - 0 = 48$

More generally, if $M$ is any upper or lower triangular matrix, then its determinant is the product of the main diagonal.

So we could have just written:

$\left\mid \begin{matrix}- 6 & 5 \\ 0 & - 8\end{matrix} \right\mid = \left(- 6\right) \left(- 8\right) = 48$