Let R be a ring that contains at least two elements. Suppose for each nonzero a in R there exists a unique b in R such that aba = a.
a. show that R has no divisors of 0
b. show that bab = b
c. show that R has unity
d. show that R is a division ring
B I worked out but I'm not sure if it works..
we're given aba = a and we need bab=b
multiply by inverse of a to get bab=b