Let $M=\left\{\left(\begin{array}{cc}x & x \ x & x\end{array} ight): x \in \mathbb{R}-\{0\} ight\

Question

Let $M=\left\{\left(\begin{array}{cc}x & x \ x & x\end{array}ight): x \in \mathbb{R}-\{0\}ight\}$. If $X, E \in M$ such that $X \cdot E=X$ for all $X \in M$, where is matrix multiplication. Then $E$ is

Professor PC Thomas Classes · Answer

Identity requirement yields $E = \begin{pmatrix} 1/2 & 1/2 \ 1/2 & 1/2 \end{pmatrix}$.