For matrices and

MATHEMATICS · Multi correct · CBSE · Mathematics · Matrices · Matrices

Problem

For

3\times3

matrices

M

and

N

, which of the following statements are not correct? (1)

N^T M N

is symmetric or skew-symmetric according as

M

is symmetric or skew-symmetric. (2)

MN-NM

is skew-symmetric for all symmetric matrices

M

and

N

. (3)

MN

is symmetric for all symmetric matrices

M

and

N

. (4)

\operatorname{adj}(M)\operatorname{adj}(N)=\operatorname{adj}(MN)

for all invertible matrices

M

and

N