To find the inverse, augment it
with the identity on the right, like this



Now use row operations to get the identity
on the left, and then the inverse will be
on the right:

Add row 1 to row 2 to get a 0 in row 2 column 1



Multiply row 1 by -2




Add row 2 to row 1:



Multiply Row 2 by 3 and Row 3 by -4



Add row 2 to row 3



Add Row 3 to Row 1



Multiply Row 3 by 3



Add Row 3 to Row 2



Divide Row 1 by -2
Divide Row 2 by 12
Divide Row 3 by -3



Now we have the identity on the left and so
the inverse is on the right:



Edwin