Problem

For

3 \times 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.

MN - NM

is skew-symmetric for all symmetric matrices

M

and

N

. c.

MN

is symmetric for all symmetric matrices

M

and

N

. d.

(\text{adj}(M))(\text{adj}(N)) = \text{adj}(M N)

for all invertible matrices

M

and

N