Find the Determinant G=[[12,0],[-6,2]]

$G = [\begin{array}{c} 12 & 0 \\ - 6 & 2 \end{array}]$

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

$determinant [\begin{array}{c} 12 & 0 \\ - 6 & 2 \end{array}] = | \begin{array}{c} 12 & 0 \\ - 6 & 2 \end{array} |$

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

$(12) (2) + 6 \cdot 0$

Simplify the determinant.

Simplify each term.

Multiply $12$ by $2$ .

$24 + 6 \cdot 0$

Multiply $6$ by $0$ .

$24 + 0$

Add $24$ and $0$ .

$24$