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(D) Given that $X$ and $Y$ are skew-symmetric,$X^T = -X$ and $Y^T = -Y$. Given that $Z$ is symmetric,$Z^T = Z$.For $(A): (Y^3 Z^4 - Z^4 Y^3)^T = (Z^4)

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$(C, D)$

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(D) Given that $X$ and $Y$ are skew-symmetric,$X^T = -X$ and $Y^T = -Y$. Given that $Z$ is symmetric,$Z^T = Z$.For $(A): (Y^3 Z^4 - Z^4 Y^3)^T = (Z^4)^T (Y^3)^T - (Y^3)^T (Z^4)^T = Z^4 (-Y)^3 - (-Y)^3 Z^4 = -Z^4 Y^3 + Y^3 Z^4 = Y^3 Z^4 - Z^4 Y^3$. This is symmetric.For $(B): (X^{44} + Y^{44})^T = (X^{44})^T + (Y^{44})^T = (X^T)^{44} + (Y^T)^{44} = (-X)^{44} + (-Y)^{44} = X^{44} + Y^{44}$. This is symmetric.For $(C): (X^4 Z^3 - Z^3 X^4)^T = (Z^3)^T (X^4)^T - (X^4)^T (Z^3)^T = Z^3 (X^T)^4 - (X^T)^4 Z^3 = Z^3 X^4 - X^4 Z^3 = -(X^4 Z^3 - Z^3 X^4)$. This is skew-symmetric.For $(D): (X^{23} + Y^{23})^T = (X^{23})^T + (Y^{23})^T = (X^T)^{23} + (Y^T)^{23} = (-X)^{23} + (-Y)^{23} = -(X^{23} + Y^{23})$. This is skew-symmetric.Thus,$(C)$ and $(D)$ are skew-symmetric.

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?
$(A) Y^3 Z^4 - Z^4 Y^3$
$(B) X^{44} + Y^{44}$
$(C) X^4 Z^3 - Z^3 X^4$
$(D) X^{23} + Y^{23}$

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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) 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}$