Find the Determinant [[-9,-7],[4,5]]

$[\begin{array}{c} - 9 & - 7 \\ 4 & 5 \end{array}]$

Step 1

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

$- 9 \cdot 5 - 4 \cdot - 7$

Step 2

Simplify the determinant.

Simplify each term.

Multiply $- 9$ by $5$ .

$- 45 - 4 \cdot - 7$

Multiply $- 4$ by $- 7$ .

$- 45 + 28$

Add $- 45$ and $28$ .

$- 17$