Find the Inverse [[2,8],[-1,-4]]

$[\begin{array}{c} 2 & 8 \\ - 1 & - 4 \end{array}]$

Step 1

Find the determinant.

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

$2 \cdot - 4 - (- 1 \cdot 8)$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $- 4$ .

$- 8 - (- 1 \cdot 8)$

Multiply $- (- 1 \cdot 8)$ .

Multiply $- 1$ by $8$ .

$- 8 - - 8$

Multiply $- 1$ by $- 8$ .

$- 8 + 8$

Add $- 8$ and $8$ .

$0$

Step 2

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