Suppose: a = b

It then follows that
a * a = a * b
a^2 = a * b
a^2 - b^2 = a * b - b^2
(a - b) * (a + b) = (a - b) * b
a + b = b
a + a = a
2 * a = 1 * a
2 = 1

Is this derivation really correct? Or is there somewhere a mistake? If so, where?

Recently, somebody told: "My grandfather was born on the first sunday of the year. His seventh birthday was also on a sunday!" In which year was this grandfather born?

A number has 6 different digits. If the last digit is moved to the front, then a new number is formed which is exaclty 5 times the old number. With which number did we start?