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Define a binary operation * on the set 0, 1, 2, 3, 4, 5as a*b = a+b if a + b< 6a+b−6 if a + b≥ 6Show that 0 is the identify for this operation and each element of the set is invertible with 6 −a being the inverse of a.i e is the identify element if a * e = e * a = aa * o = a + o = ao * a = o + a = a⇒ a * o = o * aHence, 0 is the identify of the operation.ii b is the inverse of a ifa * b = b * a = aNow, a * 6−a=a+6−a− 6=0 6−a*a=6−a+ a−6=0Hence, each element of the given set is invertible with 6−a being the inverse of a.
