1. The problem statement, all variables and given/known data Let A and B be n × n matrices. Which of the following statements are always true? (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. Some explanation for i), ii), and iii) is kindly requested. (Due to a load full of mid terms, I havn't been able to grasp the new concepts.) 2. Relevant equations det(A+B) = det(A) + det(b) 3. The attempt at a solution Well, i've carried out some examples on paper and part ii) seems to not hold true but i'm not sure if my examples would work for all applicable matrices. Part i), however, I am considering to be wrong since if we were to plug in numbers, it would make sense. e.g, det(A) = 5, det(B) = 5. Then det(5-5) = 0 Part iii) is tricky for me.