Question

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

Answer 1

`((1,1,0),(0,1,0),(0,0,1))`

Explanation:

Given
`color(white)("XXX")((1,-1,0),(0,1,0),(00,1))`
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.