# How do you find the inverse of A=((6, 4), (3, 2)) ?

Jun 30, 2016

$A = \left(\begin{matrix}6 & 4 \\ 3 & 2\end{matrix}\right)$ does not have an inverse.

#### Explanation:

For a $2 \times 2$ matrix: $M = \left(\begin{matrix}a & b \\ c & d\end{matrix}\right)$
the inverse, if it exists, is
$\textcolor{w h i t e}{\text{XXX}} {M}^{- 1} = \left(\begin{matrix}\frac{d}{\delta} & - \frac{b}{\delta} \\ - \frac{c}{\delta} & \frac{a}{\delta}\end{matrix}\right)$
where $\delta$ is the determinant of $M$

Note that in this case with $A = \left(\begin{matrix}6 & 4 \\ 3 & 2\end{matrix}\right)$
$\textcolor{w h i t e}{\text{XXX}} {\delta}_{A} = \left(6 \times 2\right) - \left(3 \times 4\right) = 0$
and since division by zero is undefined,
${A}^{- 1}$ does not exist.