Question

Use induction to prove that\[ab = ba\]

Answer 1

Let a = 3, b = 2
ab = 3*2 = 6
ba = 2*3 = 6
ab = ba

Answer 2

That's not a proof by induction :(

Answer 3

let ab=ba ,... ,n1n2=n2n1 being n=k than suppose k1k2=k2k1 is true and prove that
(k1+1)(k2+1)=(k2+1)(k1+1) so than will be
k1k2 +k1 +k2 +1 = k2k1 +k2 +k1 +1 so add to both sides -1 than will get
k1k2 +k1 +k2=k2k1 +k2 +k1 now add to both sides -k1 and get
k1k2 +k2 = k2k1 +k2 so add to both sides -k2 and get
k1k2=k2k1 so now we have get exactly what was supposed that is true so from this result that n1n2=n2n1 so ab=ba Q.E.D.
- hope so much that is right,correct !!!