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 man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

An old Woman left INR 33,333 to be divided equally among two fathers and two sons and each was to receive INR 11,111.
How was this possible?

John leaves home and then he takes three right turns. John wants to return to home but he was scared of Jacob, who is wearing a mask.

What is John Situation ?

What breaks yet never falls, and what falls yet never breaks?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

If 2 workers can complete painting 2 walls in exactly 2 hours.

How many workers would be needed to paint 18 walls in 6 hours?

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?

A man and a dog were going down the street. The man rode, yet walked. What was the dog’s name?

There was a blind beggar living on the footpath of a street. Suddenly one day, the beggar's brother died. What was the relation of the blind beggar with the person who died?

PS: Brother is not the answer.