Question

If $\left[\begin{array}{cc}{e}^x& e^y\\ e^y& e^x\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$ , then the values of $x$ and $y$ are respectively :

• A. $-1,-1$
• B. $1,1$
• C. $0,1$
• D. $1,0$
• E. $0,0$

Answer 1

The correct option is E $0,0$

Given, $\left[\begin{array}{cc}{e}^x& e^y\\ e^y& e^x\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}{e}^x& e^y\\ e^y& e^x\end{array}\right]=\left[\begin{array}{cc}{e}^0& e^0\\ e^0& e^0\end{array}\right]$ ....$(\because e^0=1)$
On equating the corresponding elements, we get
$e^x=e^0$ and $e^y=e^0$
$\therefore x=0andy=0$