Find the Determinant [[3,4],[6,5]]

$[\begin{array}{c} 3 & 4 \\ 6 & 5 \end{array}]$

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

$determinant [\begin{array}{c} 3 & 4 \\ 6 & 5 \end{array}] = | \begin{array}{c} 3 & 4 \\ 6 & 5 \end{array} |$

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

$(3) (5) - 6 \cdot 4$

Simplify the determinant.

Simplify each term.

Multiply $3$ by $5$ .

$15 - 6 \cdot 4$

Multiply $- 6$ by $4$ .

$15 - 24$

Subtract $24$ from $15$ .

$- 9$