Question: Let R be a ring that contains at least two elements. Suppose for each nonzero a R, there exists a unique b R

Let R be a ring that contains at least two elements. Suppose for each nonzero a ∈ R, there exists a unique b ∈ 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.

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