Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

They are three errirs in this question. Can you find them?

What always comes into a house through the keyhole?

A person was killed at a house party. When the police arrive, there are six people present in the house who are the friends of the victim. The name of the friends is Rohit, Aman, Nick, Gagan, and Randy.

Near the dead body, they find a few numbers written with blood by the victim on the floor. The numbers are 8, 5, 4, and 11.

The police arrests one of the friends for the murder. Whom did they arrest and why?

Using Only Five 5's and any mathematical operator make sum as 37

You are playing as white and given four rooks to checkmate the black king in four moves with the following rules 1. You can place one rook every move and ensure the black king should be in check position.2. After four moves the black king should be in the checkmate position.

John replied, when asked how old he was. In 2 years he will be twice as old as he was five years ago.' How old is he ?

Which flower has two lips?