In algebra a equals b (a=b) can 2=1?

Question

a squared - b squared= ab-b squared

equal 2=1

Answer 1

hahahaha. ok

let's say a=b

then we could multiply each side by a, value stays the same.

a^2=ab

now we'll subtract b^2 from each side, it doesnt change value.

a^2-b^2=ab-b^2

now we can factor

(a+b)(a-b)=b(a-b)

now, divide each side by (a-b)

a+b=b

so if we go back to the beginning, a=b, and if a=1,  2=1

But wait, the flaw is in the last step, dividing by (a-b), since that is dividing by zero. Math doesnt allow you to divide by zero.