Generating integer matrices with integer inverses For certain simulations, it is con venient to have a collection of randomly-generated matrices that have integer entries and whose inverses also have integer entries. Argue, using Theorem 14, that an integer matrix with determinant equal to 1 or - will have an integer inverse. One easy way to create an integer matrix A with determinant equal to 1 or -1 is to set A LU where L is a lower-triangular integer matrix with l's and -'s on its diagonal and where U is an upper-triangular integer matrix with l's and -1's on its diagonal. Then, since det(A) det(L) det(U), we see that both A and A will be integer matrices Use these ideas to create a set of ten randomly generated (5 x 5) integer matrices with integer inverses. For each matrix A created, use the MATLAB inv command to generate the inverse for A. Note, because of roundoff error, that the MATLAB inverse for A is not always an integer matrix. To eliminate the roundoff error, you can use the command round (inv (A)) in order to round the entries of A-1 to the nearest integer. Check, by direct multiplication, that this will produce the inverse.