\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Find the values of \(x\) and \(y\) for which the following matrix equality holds:$$ \begin{pmatrix} x & y \\ y & x \end{pmatrix} = \begin{pmatrix} y & -x \\ -x & y \end{pmatrix} $$
\(x = \)
\(\quad\) and \(\quad\) \(y = \)