Find the Inverse [[5,10],[2,4]]

$[\begin{array}{c} 5 & 10 \\ 2 & 4 \end{array}]$

Step 1

Find the determinant.

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

$5 \cdot 4 - 2 \cdot 10$

Simplify the determinant.

Simplify each term.

Multiply $5$ by $4$ .

$20 - 2 \cdot 10$

Multiply $- 2$ by $10$ .

$20 - 20$

Subtract $20$ from $20$ .

$0$

Step 2

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