If matrix A= […] and A^T=A , then

The correct answer is Option (1) → \( x=y \)

The condition \( A^{T}=A \) says that \( A \) is a symmetric matrix.

So the entries placed symmetrically about the diagonal must be equal.

Here those entries are \( a_{12}=x \) and \( a_{21}=y \), which gives \( x=y \).