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QUESTION
Let G = GL2(R) and H = SL2(R). Prove that, for any a, b in G, the cosets aH and bH are equal if and only if det(a) = det(b). Hint:
Let G = GL2(R) and H = SL2(R). Prove that, for any a, b in G, the cosets aH and bH are equal if and only if det(a) = det(b).
Hint: You may use the fact that det(xy) = det(x)det(y) for all x, y ∈ GL2(R).
