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`.

Options

A. `N^(T)` M N is a symmetric or skew symmetricm according as M is symmetric or skew symmetric
B. MN-NM is skew symmetric for all symmetric matrices M and N
C. M N is symmetric for al symmetric matrices M and N
D. (adj M)(adj N)=adj(MN) for all invertible matrices M and N

Answer

C, D