# Is 2=1?

**Algebra**Level 2

Following are some steps to prove that 2=1 :

**Step 1:** Let A = B

**Step 2:** Multiply both sides by A:-
A² = AB

**Step 3:** Subtract B² from both sides:-
A² - B² = AB - B²

**Step 4:** Factorize both sides:-
( A + B )( A - B ) = B ( A - B )

**Step 5:** Divide both sides by ( A - B ) to obtain
A + B = B

**Step 6:** Since A = B hence
B + B = B

**Step 7:** Simplify to obtain
2B = B

**Step 8:** Divide both sides by B to obtain
2=1.............hence proved.

Which step in the proof is **mathematically wrong**?