Question

Let A and B be n × n matrices. Which of the following statements are always true?

Answer 1

(i) If det(A) = det(B) then det(A − B) = 0.
(ii) If A and B are symmetric, then the matrix AB is also symmetric.
(iii) If A and B are skew-symmetric, then the matrix AT + B is also skew-symmetric.

Answer 2

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