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

Feb 18, 2016

$\left(\begin{matrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right)$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \left(\left(1 , - 1 , 0\right) , \left(0 , 1 , 0\right) , \left(00 , 1\right)\right)$
Extend this matrix by appending an identity matrix on the right side:
color(white)("XXX")((1,-1,0,"|",1,0,0),(0,1,0,"|",0,1,0),(0,0,1,"|",0,0,1))

Perform standard row operations to convert the left side into an identity matrix.
In this case all that is needed is to add Row 2 to Row 1:
color(white)("XXX")((1,0,0,"|",1,1,0),(0,1,0,"|",0,1,0),(0,0,1,"|",0,0,1))

and the left side is the required inverse.