Assertion , \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x}_{1} \\ \boldsymb

Assertion \( \operatorname{Let} \boldsymbol{A}=\left[\begin{array}{ll}\boldsymbol{a}_{11} & \boldsymbol{a}_{12} \\ \boldsymbol{a}_{21} & \boldsymbol{a}_{22}\end{array}\right], \boldsymbol{X}=\left[\begin{array}{l}\boldsymbol{x}_{1} \\ \boldsymbol{x}_{2}\end{array}\right], \boldsymbol{y}= \) \( \left[\begin{array}{l}\boldsymbol{y}_{1} \\ \boldsymbol{y}_{2}\end{array}\right. \) If \( A \) is symmetric, then \( X^{\prime} A Y=Y^{\prime} A X \) for each pair of \( X \) and \( Y \) Reason If \( \boldsymbol{X}^{\prime} \boldsymbol{A} \boldsymbol{Y}=\boldsymbol{Y}^{\prime} \boldsymbol{A} \boldsymbol{X} \) for each pair of \( \boldsymbol{X} \) and \( Y, \) then \( A \) is symmetric.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct