Let A be a ring with property : for every $\displaystyle a \in A $ , exist $\displaystyle K \in N $ s.t $\displaystyle a^{2k}=a $ . Prove that :
a) $\displaystyle |A|$ is a power of 2
b) $\displaystyle \sum_{\substack{
a \in A \\}} a =0$