Let be matrices such that is symmetric and and are skew-symmetric. Consider the statements is symmetric is symmetric Then,

Only is true Explanation: Solution: Given Information: is symmetric: and are skew-symmetric: and Key Properties used: Step 1: Statement (S1) Check Check if is symmetric ( ). Since (as power is even) and : Dhyan dein, yaha aaya hai, iska matlab (S1) Skew-Symmetric hai, symmetric nahi. Isliye (S1) False hai. Step 2: Statement (S2) Check Check if is symmetric. Since (as power is odd) and : Yaha aaya hai, iska matlab (S2) Symmetric hai. Isliye (S2) True hai. Conclusion: (S1) is False (S2) is True Correct Option: (1) Only S2 is true

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $A, B, C$ be $3 \times 3$ matrices such that $A$ is symmetric and $B$ and $C$ are skew-symmetric. Consider the statements

$(S1)$ $A^{13} B^{26} - B^{26} A^{13}$ is symmetric

$(S2)$ $A^{26} C^{13} - C^{13} A^{26}$ is symmetric

Then,

Choose the correct answer: