Determine whether the given set of invertible n x n matrices with real number entries is a subgroup of GL(n, R).

The set of all n x n matrices A such that (A^T)A = l_n • [These matrices are called orthogonal. Recall that A^T, 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 = (B^T)(A^T).]