How Do You Test The Inverse Of A Matrix?
After going through all the work to find the inverse of a matrix it is nice to be able to check it, using this technique on a test is very important. First off you need a matrix inverse to test. Augment the matrix with the identity matrix and get it in reduced echelon form. Then you have your possible inverse, you should always test it. To test it you need to multiply the original matrix and the possible inverse together. After going through all the multiplication you should end up with the identity matrix. If not you probably made an error in multiplication or in finding you matrix, good thing you were checking it. If multiplying the matrices together has resulted in the identity matrix, then you must multiply the matrices again but in the other direction. The same rules as before apply, when the second multiplication is equal to the identity matrix then you can be sure that it is the right answer.
