1. The problem statement, all variables and given/known data Let ab=a and ba=b, show that a^2 = a and that b^2 = b 2. Relevant equations none 3. The attempt at a solution Not sure if I did this correct.. but here is what I did. Given: ab = a. Multiply both by left hand multiplication by a^-1 a^-1*a*b = 1. where a^-1*a is obviously the identity. so b = 1. Given: ba = b. Multiply both by left hand multiplication by b^-1. b^-1*b*a = 1 1a=1 a=1 so a =1. If b = 1 and a=1, then b^2 = 1 and a^2 = 1, so a^2 = a and b^2 = 2. Did I do this correctly?