JEE-Advanced 2015 (9/40)

Algebra Level 5

Let XX and YY be two arbitrary, 3×33 \times 3, non-zero, skew-symmetric matrices and ZZ be an arbitrary, 3×33 \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)(1),(2), then submit 12 as the correct answer, if your answer is (2),(3),(4)(2),(3),(4), then submit 234 as the correct answer.

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