Arguably the reason why high school students commit suicide, and the most difficult concept of Algebra 2. A complete waste of time, as there are various other methods of solving matrices that don't involve half-hour long porcesses that are very liable to error.
Test on augmented matricies: Augment the Matrix:
( 2 4 5 | 5 )
( 1 3 3 | 2 )
( 2 4 6 | 2 )
Student: "OH LORD JESUS HAVE MERCY!" /uses Kramer's rule anyway