Math Logic Puzzle: 1=0 and 1=2

The following are three mathematical proofs; in all three proofs, each step is justified by a mathematical rule or theorem. Perhaps, when I have more time, I will write the justification (rule or theorem) for each step next to each equation. ‘Till then, challenge them as they are!

Way #1

a=0
a^2=0
a-a=0
(a^2)-a=0
\ a-a=(a^2)-a
a=a^2
a/a=(a^2)/a
1=a
\1=0

Way #2

a=0
a^2=0
(a^2)-a=0
a(a-1)=0
(a(a-1))/a=0/a
a-1=0
\ a=1
\ 1=0

Way #3

assume a=2
a-2=0
a-2+1=0+1
a-1=1
if a-2=0, then
(a-2)(a-1)=(0)(1)
(a-2)(a-1)=0
((a-2)(a-1))/(a-2)=0/(a-2)
a-1=0
a=1
\1=2