Solution

9. (Tutorial-work) Determine if each of the following statement holds true as subgroups of GL. (R), the the general linear group of n x n matrices with real entries. (a) n x n matrices with determinant 2. (b) n x n diagonal matrices with no zeros on the diagonal. (c) n x n matrices with determinant +1. (d) n x n matrices A such that AT A = In where AT = (aji) is the transpose of A = (aij).