Let X and Y be two arbitrary, 3×3, non – zero, skew – symmetric matrices and Z be an arbitrary 3×3  , non – zero, symmetric matrix. Then which of the following matrices is(are) skew symmetric

Given XT=-X, YT=-Y, ZT=ZY3Z4-Z4Y3T=Y3Z4T-Z4Y3T=ZT4YT3-YT3ZT4=Z4(-Y)3-(-Y)3(Z)4=-Z4Y3+Y3Z4=-Z4Y3-Y3Z4⇒Notskew-symmetricX44+Y44T=YT4+YT4=(-X)44+(-Y)44=X44+Y44⇒SymmetricX4Z3-Z3X4T=ZT3XT4-XT4ZT3=Z3(-X)4-(-X)4(Z)3=Z3X4-X4Z3=-X4Z3-Z3X4⇒Skewsymmetric X23+Y23T=XT23+YT23=(-X)23+(-Y)23=-X23-Y23=-X23+Y23⇒Skew-symmetric