Determine whether the following three sets are a subspace of Rn. If it is, show that the the 3 subspace properties are satisfied, and if it is not, show by example that one of the properties fails.

1. The set of solutions of Ax= x, where A is any n x n matrix.

2. The first quadrant in R2. That is: {[x_1, x_2] ∈ R2| x_1 ≥ 0 and x_2 ≥ 0}

3. {[x_1, x_2] ∈ R2| (x_1 ≥ 0 and x_2 ≥ 0) or (x_1 0 ≤ and x_2 ≤ 0)}