Let ℝ denote the set of all real numbers and let i = √−1. Consider the matrices S = [[0, −1], [1, 0]] and T = [[1, 1], [0, 1]]. Let a, b, c, d be real numbers such that ST = [[a, b], [c, d]]. Let H = {x + iy : x, y ∈ ℝ and y > 0}. Then which of the following statements is (are) TRUE?