Algebra Level 5

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 ? $\begin{array}{} (1) \, Y^3Z^4-Z^4Y^3 \quad \quad \quad \quad & (2) \, X^{44}+Y^{44} \\ (3) \, X^4Z^3-Z^3X^4 & (4) \, X^{23}+Y^{23} \end{array}$
Note :

• Submit your answer as the increasing order of the serial numbers of all the correct options.

• For eg, if your answer is $$(1),(2)$$, then submit 12 as the correct answer, if your answer is $$(2),(3),(4)$$, then submit 234 as the correct answer.

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