If $A = \begin{bmatrix} 5 & x \\ y & 0 \end{bmatrix}$ and $A = A^T$, where $A^T$ is the transpose of the matrix $A$, then:

$x = y$

The correct answer is Option (2) → $x = y$ ##

$A = \begin{bmatrix} 5 & x \\ y & 0 \end{bmatrix}$, $A^T = \begin{bmatrix} 5 & y \\ x & 0 \end{bmatrix}$

Since $A = A^T$:

$\begin{bmatrix} 5 & x \\ y & 0 \end{bmatrix} = \begin{bmatrix} 5 & y \\ x & 0 \end{bmatrix}$

$∴x = y$