GRE Exam Numerical Ability Data Sufficiency

Let A be a real 2*2 matrix. Which of the following statements must be true?
I. All of the entries of A^2 are nonnegative.
II. The determinant of A^2 is nonnegative.
III. If A has two distinct eigenvalues, then A^2 has two distinct eigenvalues.
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III

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GRE Other Question

Up to isomorphism, how many additive abelian groups G of order 16 have the property that x+x+x+x = 0
for each x in G ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5 If A is a subset of the real line R and A contains each rational number, which of the following must be true?
(A) If A is open, then A = R.
(B) If A is closed, then A = R.
(C) If A is uncountable, then A = R .
(D) If A is uncountable, then A is open.
(E) If A is countable, then A is closed.