The identity element in the group M = left{ b | vedclass

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(B) Let $E = \begin{bmatrix} a & a \ a & a \end{bmatrix}$ be the identity element in the set $M$ such that for any matrix $A = \begin{bmatrix} x & x

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$\frac{1}{2} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$

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(B) Let $E = \begin{bmatrix} a & a \ a & a \end{bmatrix}$ be the identity element in the set $M$ such that for any matrix $A = \begin{bmatrix} x & x \ x & x \end{bmatrix} \in M$,we have $A \cdot E = A$. Performing the matrix multiplication: $\begin{bmatrix} x & x \ x & x \end{bmatrix} \begin{bmatrix} a & a \ a & a \end{bmatrix} = \begin{bmatrix} xa+xa & xa+xa \ xa+xa & xa+xa \end{bmatrix} = \begin{bmatrix} 2ax & 2ax \ 2ax & 2ax \end{bmatrix}$. Equating this to $A$: $\begin{bmatrix} 2ax & 2ax \ 2ax & 2ax \end{bmatrix} = \begin{bmatrix} x & x \ x & x \end{bmatrix}$. This implies $2ax = x$. Since $x 
eq 0$,we can divide by $x$ to get $2a = 1$,which means $a = \frac{1}{2}$. Thus,the identity element is $\begin{bmatrix} 1/2 & 1/2 \ 1/2 & 1/2 \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}$.

The identity element in the group $M = \left\{ \begin{bmatrix} x & x \\ x & x \end{bmatrix} \mid x \in \mathbb{R}, x \neq 0 \right\}$ with respect to matrix multiplication is

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