Find the Inverse [[-4,-6],[8,12]]

$[\begin{array}{c} - 4 & - 6 \\ 8 & 12 \end{array}]$

Step 1

Find the determinant.

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

$- 4 \cdot 12 - 8 \cdot - 6$

Simplify the determinant.

Simplify each term.

Multiply $- 4$ by $12$ .

$- 48 - 8 \cdot - 6$

Multiply $- 8$ by $- 6$ .

$- 48 + 48$

Add $- 48$ and $48$ .

$0$

Step 2

There is no inverse because the determinant is $0$ .