Find the Determinant [[5,3],[-1,-3]]

$[\begin{array}{c} 5 & 3 \\ - 1 & - 3 \end{array}]$

Step 1

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

$5 \cdot - 3 - (- 1 \cdot 3)$

Step 2

Simplify the determinant.

Simplify each term.

Multiply $5$ by $- 3$ .

$- 15 - (- 1 \cdot 3)$

Multiply $- (- 1 \cdot 3)$ .

Multiply $- 1$ by $3$ .

$- 15 - - 3$

Multiply $- 1$ by $- 3$ .

$- 15 + 3$

Add $- 15$ and $3$ .

$- 12$