You can generate unimodular matrices by entering a matrix A and giving the instruction [D,M,N] = quick(A) to find not one but two unimodular matrices M and N. (Ignore D.)
Use a unimodular matrix generated in this way to try out the method of Exercise 17 for inverting unimodular matrices. In other words, apply `algo' (or `algo2' or `quick') to a unimodular matrix A to find unimodular matrices M and N such that MAN is an identity matrix. Then check that the matrix B defined by B = N*M has the property that both AB and BA are identity matrices.
If A is unimodular, then application of either `algo' or `algo2' to A will normally terminate with the identity matrix, but there are exceptions. Try to find an exception. (See When are diagonal matrices equivalent?) If M, A, and N are all unimodular, and MAN is diagonal but not an identity matrix, then NM is not an inverse of A, but an inverse of A can still be found using M, N, and A. Try to find a method.
Return to Chapter 2.