Help me finding the inverse?

Question

Find the inverse of the given matrix by using gauss-jordan elimination.
A=[1 0 1]
[0 1 1]
[1 1 0]

Answer 1

Follow the example below.
you have to form the inverse by reducing your matrix to a unit matrix.
1 0 0 a b c
0 1 0 d e f
0 0 1 g h i

Answer 2

Lets start by putting the unit matrix next to it:
[1 0 1][1 0 0]
[0 1 1][0 1 0]
[1 1 0][0 0 1]

Subtract the 1st row from the 3rd
[1 0 1][1 0 0]
[0 1 1][0 1 0]
[0 1 -1][-1 0 1]

Add the 3rd row from the 2nd
[1 0 1][1 0 0]
[0 2 0][-1 1 1]
[0 1 -1][-1 0 1]

Divide the 2nd row by 2
[1 0 1][1 0 0]
[0 1 0][-1/2 1/2 1/2]
[0 1 -1][-1 0 1]

Subtract the 2nd row from the 3rd

[1 0 1][1 0 0]
[0 1 0][-1/2 1/2 1/2]
[0 0 -1][-1/2 -1/2 1/2]

Add the 3rd row to the 1st
[1 0 0][1/2 -1/2 1/2]
[0 1 0][-1/2 1/2 1/2]
[0 0 -1][-1/2 -1/2 1/2]

Multiply the 3rd row by -1
[1 0 0][1/2 -1/2 1/2]
[0 1 0][-1/2 1/2 1/2]
[0 0 1][1/2 1/2 -1/2]

A^-1 is:
[1/2 -1/2 1/2]
[-1/2 1/2 1/2]
[1/2 1/2 -1/2]