jee-advanced 2015 Q49

jee-advanced · India · paper1 Matrices Matrix Algebra and Product Properties

Let $X$ and $Y$ be two arbitrary, $3 \times 3$, non-zero, skew-symmetric matrices and $Z$ be an arbitrary $3 \times 3$, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?
(A) $\quad Y ^ { 3 } Z ^ { 4 } - Z ^ { 4 } Y ^ { 3 }$
(B) $X ^ { 44 } + Y ^ { 44 }$
(C) $X ^ { 4 } Z ^ { 3 } - Z ^ { 3 } X ^ { 4 }$
(D) $X ^ { 23 } + Y ^ { 23 }$

Let $X$ and $Y$ be two arbitrary, $3 \times 3$, non-zero, skew-symmetric matrices and $Z$ be an arbitrary $3 \times 3$, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?\\
(A) $\quad Y ^ { 3 } Z ^ { 4 } - Z ^ { 4 } Y ^ { 3 }$\\
(B) $X ^ { 44 } + Y ^ { 44 }$\\
(C) $X ^ { 4 } Z ^ { 3 } - Z ^ { 3 } X ^ { 4 }$\\
(D) $X ^ { 23 } + Y ^ { 23 }$

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