Thank you for reporting, we will resolve it shortly
Q.
The identity element in the group $M = \left\{
\begin{bmatrix}
x & x \\
x & x\\
\end{bmatrix} | x \ \in \ R, x \neq 0 \right\}$ with respect to matrix multiplication is
$M=\begin{bmatrix}x & x \\ x & x\end{bmatrix}, \forall x \in R$ and $x \neq 0$
Let $P$ be the identity element in the group
i.e. $P=\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2}\end{bmatrix}=\frac{1}{2}\begin{bmatrix}1 & 1 \\ 1 & 1\end{bmatrix}$
$P$ is obtained by putting $x=\frac{1}{2}$
$\therefore \, M P=\begin{bmatrix}x & x \\ x & x\end{bmatrix}\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2}\end{bmatrix}=M$
and $PM=\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{1}{2}\end{bmatrix}\begin{bmatrix}x & x \\ x & x\end{bmatrix}=M$
$\therefore \, M P=M=P M$