Find the Determinant [[-5,-2],[8,-3]]

$[\begin{array}{c} - 5 & - 2 \\ 8 & - 3 \end{array}]$

These are both valid notations for the determinant of a matrix.

$determinant [\begin{array}{c} - 5 & - 2 \\ 8 & - 3 \end{array}] = | \begin{array}{c} - 5 & - 2 \\ 8 & - 3 \end{array} |$

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$(- 5) (- 3) - 8 \cdot - 2$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $- 3$ .

$15 - 8 \cdot - 2$

Multiply $- 8$ by $- 2$ .

$15 + 16$

Add $15$ and $16$ .

$31$