The Cayley Hamilton is a nifty procedure to find the inverse of a matrix using
the characteristic polynomial of a given square matrix. So no Row Echolon or similar is needed.
We just included this Cayley Hamilton in the Linear Algebra Made Easy TI89. Best of all complete steps are shown until the inverse matrix is found.
If you have been using Linear Algebra Made Easy, please redownload this updated app at www.ti89.com/apps and simply replace the existing app.
You may refresh your memory about the procedure here