Show that a*b=b*a

Prob. Let ({a, b}, * ) be a semigroup where aa =b. Show that- ab=b*a.

Sol.

Given

({a*b}, *) is a semigroup

And a*a = b.

Now

ab = a(aa) (∵ aa=b)

ab =(aa)*a (by associative law)

ab =ba (∵ a*a=b)