For 3 X 3 matrices M and N which of the following statements is (are ) false
(a) $N^TMN $ is a symmetric or skew symmetric , according as M is symmetric or skew symmetric.
(b) MN-NM is skew symmetric $\forall$ symmetric matrices M and N.
(c) MN is symmetric $\forall$ symmetric matrices M and N .
(d) (adjM)(adjN) = adj(MN) $\forall$ invertible matrices M and N.
(a) I tried to solve it algebrically by using 2X2 matrices rather using 3X3 matrices ( I hope result will not vary due to this) and found it is false, it also depends on N as well. ( Please verify this assertion thanks..)
(b) I am getting the value of MN -NM =0 matrix , so it is a null matrix . please confirm the result then... I think it is false.
(c) It is true..
(d) For this please guide... thanks... a lot..