jee-advanced 2013 Q52

jee-advanced · India · paper1 Matrices True/False or Multiple-Select Conceptual Reasoning
For $3 \times 3$ matrices $M$ and $N$, which of the following statement(s) is (are) NOT correct?
(A) $\quad N ^ { T } M N$ is symmetric or skew symmetric, according as $M$ is symmetric or skew symmetric
(B) $M N - N M$ is skew symmetric for all symmetric matrices $M$ and $N$
(C) $M N$ is symmetric for all symmetric matrices $M$ and $N$
(D) $\quad ( \operatorname { adj } M ) ( \operatorname { adj } N ) = \operatorname { adj } ( M N )$ for all invertible matrices $M$ and $N$
For $3 \times 3$ matrices $M$ and $N$, which of the following statement(s) is (are) NOT correct?\\
(A) $\quad N ^ { T } M N$ is symmetric or skew symmetric, according as $M$ is symmetric or skew symmetric\\
(B) $M N - N M$ is skew symmetric for all symmetric matrices $M$ and $N$\\
(C) $M N$ is symmetric for all symmetric matrices $M$ and $N$\\
(D) $\quad ( \operatorname { adj } M ) ( \operatorname { adj } N ) = \operatorname { adj } ( M N )$ for all invertible matrices $M$ and $N$