Chapter 5 - Determinants, Inverses, and Cramer’s Rule

Section 5.5 -  Inverses from rref

Example 5.5.1

(A={{-9,3,0,2,-4,5,1},{6,8,-7,-1,2,10,3},{2,5,-1,-15,6,2,-4},{11,7,5,4,-8,-1,6},{-7,1,1,2,5,-3,8},{1,-12,9,0,4,-2,13},{0,-9,7,2,6,3,-4}})//MatrixForm

(Id7=IdentityMatrix[7])//MatrixForm

(AId7=Join[A,Id7,2])//MatrixForm

RRAId7=RowReduce[AId7];

Drop[RRAId7,{},{1,7}]//MatrixForm

Inverse[A]//MatrixForm