Maths Matrices and Determinants JEE (Advanced) / IIT - JEE Problems ( Previous Year ) More Than One Correct MCQ
Published on: August 13, 2026

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

A
N T M N is symmetric or skew symmetric, according as M is symmetric or skew symmetric
B
M N – N M is skew symmetric for all symmetric matrices M and N
C
M N is symetric for all symmetric matrices M and N
D
(adj M) (adj N) = adj(MN) for all invertible matrices M and N

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The correct answer is:
CHECK THE SOLUTION.

(c,d)

(N T MN) T = N T M T N is symmetric if M is symmetric and skew-symmetric if M is skew-symmetric.

(MN – NM) T = (MN) T – (NM) T = NM – MN = – (MN – NM)

skew symmetric

(MN) T = N T M T = NM ≠ MN hence NOT correct

standard result is

adj(MN) = (adjN) (adj M)] ≠ (adjM) (adjN)

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