More from devadas v

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(21), Theorem al a, O if, Z and a, arre elerants is IR with, 2+a =a,, then, 6 If, u and bto are, elecerts in IR, with, u.b = b, the, %3D, If, a e R,, then, a: O = O, Proof:, Suppose that, Z+a, have, that, 2= 0, lie, Uniqueness, to, prove, Cwe, of, additive, identity), Csives that, Z+a s a, (2+9) +E4) = g Ga), a +(-4) ( adding, (-a), on bothsides, 2+ Ca +ea), ( by associative loue, Ered Eristere of, ioverse), Z+ O, Suppose, that, u. b =b, where, a#9, uniqueneas of, we, have to p.T, Cie, roultiplicative, datity), Coiven that, u.b = b, for bi#o, (ub).t = bit, (:! b#0, multipli -, Cabi ve inverse, E erist