Find the Inverse [[2,3],[4,6]]

$[\begin{array}{c} 2 & 3 \\ 4 & 6 \end{array}]$

Step 1

Find the determinant.

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

$2 \cdot 6 - 4 \cdot 3$

Simplify the determinant.

Simplify each term.

Multiply $2$ by $6$ .

$12 - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$12 - 12$

Subtract $12$ from $12$ .

$0$

Step 2

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