Question

In exercise 8 through 13, determine whether the given set of invertible n x n matrices with real numbers entries is a subgroup of GL (n, R)
11. Then n x n matrices with determinant -1
13. The set of all n x n matrices A such that (AT) A = In. [These matrices are called orthogonal. Recall that AT, the transpose of A, is the matrix whose jth column is the jth row of A for 1 ≤ j ≤ n, and that the transpose operation has the property (AB)T = (BT)(AT).]

Answer 1

What is required to make those sets of matrices subgroups of GL(n,R) ?