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For 3xx3 matrices M \ a n d \ N , which ...

For `3xx3` matrices `M \ a n d \ N ,` which of the following statement (s) is (are) NOT correct ?
Statement - I : `N^T M N` is symmetricor skew-symmetric, according as `M` is symmetric or skew-symmetric.
Statement - II : `M N-N M` is skew-symmetric for all symmetric matrices `Ma n dN`.
Statement - III : `M N` is symmetric for all symmetric matrices `M a n dN`.
Statement - IV : `(a d jM)(a d jN)=a d j(M N)` for all invertible matrices `Ma n dN`.

A

`N^T MN` is symmetric or skew-symmetric, according as M is symmetric or skew-symmetric

B

MN-NM is symmetric for all symmetric matrices M and N

C

MN is symmetric for all symmetric matrices M and N

D

(adj M) (adjN) = adj(MN) for all invertible matrices M and N

Text Solution

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The correct Answer is:
C, D
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