# How do you find the inverse of [(-4,6), (8,-12)]?

Jan 18, 2017

The matrix is not invertible.

#### Explanation:

The inverse of the matrix $A = \left(\begin{matrix}a & b \\ c & d\end{matrix}\right)$ is

${A}^{-} 1 = \frac{1}{a d - b c} \cdot \left(\begin{matrix}d & - b \\ - c & a\end{matrix}\right)$

Here,

$A = \left(\begin{matrix}- 4 & 6 \\ 8 & - 12\end{matrix}\right)$

We calculate the determinant

$D e t A = | \left(- 4 , 6\right) , \left(8 , - 12\right) | = \left(- 4 \cdot - 12\right) - \left(6 \cdot 8\right) = 48 - 48 = 0$

As $D e t A = 0$, the matrix is not invertible