JEE Advanced 2013 Mathematics question

For 3 × 3 matrices M and N, which of the following statement(s) is (are) **NOT** correct ?

(A) is symmetric or skew symmetric, according as M is symmetric or skew symmetric
(B)MN − NM is skew symmetric for all symmetric matrices M and N
(C)MN is symmetric for all symmetric matrices M and NCorrect
(D)(adj M)(adj N) = adj (MN) for all invertible matrices M and NCorrect

Answer: (C),(D)

Solution

(A) , which equals if and if : correct. (B) (MN - NM)^T = N^TM^T - M^TN^T = NM - MN = -(MN - NM): skew symmetric, correct. (C) , which equals MN only when M and N

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Question ID VK-026175