
1.6.89 Fields, Groups, Rings
condition: Let \( B \) be a subgroup in \( G L_{2}(\mathbb{R}) \) consisting of upper triangular matrices, and \( U- \) be a subgroup in \( B \) consisting of matrices with ones on the main diagonal. Prove that \( B / U \cong \mathbb{R}^{*} \times \mathbb{R}^{*} \).