# How do you find the inverse of [(0,0), (-1,8)]?

Nov 30, 2016

$\left[\frac{8}{0} \frac{0}{0} \frac{1}{0} \frac{0}{0}\right]$

#### Explanation:

Sorry, i'm not sure on how to get this to look how you have it in matrix form.

The first step is to flip the numbers in the main diagonal and then flip the operator signs of the second diagonal, eg. -1 becomes 1.

Multiplying the two numbers in the main diagonal and subtracting this answer from from the product of the second diagonal.

In this case both products are 0, so ${A}^{-} 1 \left(\frac{1}{0}\right)$

8/0 0/0
1/0 0/0

Hope this helps.

Dec 7, 2016

This matrix has no inverse

#### Explanation:

Note that:

$\left\mid \begin{matrix}0 & 0 \\ - 1 & 8\end{matrix} \right\mid = 0 \cdot 8 - 0 \cdot \left(- 1\right) = 0 - 0 = 0$

Since the determinant is zero, this matrix has no inverse.

In general:

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

but if $\left\mid \begin{matrix}a & b \\ c & d\end{matrix} \right\mid = 0$ then there is no inverse.