# JEE-Advanced 2015 (9/40)

**Algebra**Level 4

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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