b
(b) Let $\left[ {\begin{array}{*{20}{c}}a&a\\a&a\end{array}} \right]$be the identity element then
$\left[ {\begin{array}{*{20}{c}}x&x\\x&x\end{array}} \right]\left[ {\begin{array}{*{20}{c}}a&a\\a&a\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}x&x\\x&x\end{array}} \right]$
i.e., $2ax = x \Rightarrow a = \frac{1}{2}$,
Identity element = $\frac{1}{2}\left[ {\begin{array}{*{20}{c}}1&1\\1&1\end{array}} \right]$.