Find inverse of the matrix using the inversion algorithm.

Subtract 3 times the first row from the second row, and replace the second row.
Subtract 4 times the first row from the third row, and replace the third row.
This gives



Now add (-4) times the third row to 5 times the second row, and replace the third row.
This gives



Multiply the third row by -1/2.



Next, add 2 times the third row to the second row, and replace the second row.



Multiply the second row by -1/4.



Finally, add (-2) times the second row and (-1) times the third row to the first row, and replace the first row. You'll end up with



So the inverse is