0, 0
Given, \(\begin{bmatrix}e^{x} & e^{y} \\ e^{y} & e^{x}\end{bmatrix}=\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}\)
\(\Rightarrow \begin{bmatrix}e^{x} & e^{y} \\ e^{y} & e^{x}\end{bmatrix}=\begin{bmatrix}e^{0} & e^{0} \\ e^{0} & e^{0}\end{bmatrix} (\because e^{0}=1)\)
On equating the corresponding elements,
\(e^{x}=e^{0}\) and \(e^{y}=e^{0}\)
\(\Rightarrow x=0\) and \(y=0\)
So, the correct option is (B): 0, 0
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.