Latest GRE Aptitude Question SOLUTION: 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 t

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Previous 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 Next Question: 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.

(#M40151774) GRE Numerical Ability question Matrix Keep an EYE

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: Asked In GRE Aashu (9 years ago); Unsolved; Is this Puzzle helpful? (0) (0) Submit Your Solution Data Sufficiency

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Previous 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 Next Question: 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.

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