Find the Determinant [[-5,2],[4,6]]

$[\begin{array}{c} - 5 & 2 \\ 4 & 6 \end{array}]$

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

$determinant [\begin{array}{c} - 5 & 2 \\ 4 & 6 \end{array}] = | \begin{array}{c} - 5 & 2 \\ 4 & 6 \end{array} |$

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

$(- 5) (6) - 4 \cdot 2$

Simplify the determinant.

Simplify each term.

Multiply $- 5$ by $6$ .

$- 30 - 4 \cdot 2$

Multiply $- 4$ by $2$ .

$- 30 - 8$

Subtract $8$ from $- 30$ .

$- 38$