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

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?

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

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

A man is looking at a photograph of someone. His friend asks who it is. The man replies, “Brothers and sisters, I have none. But that man’s father is my father’s son.” Who was in the photograph?

I am not alive, but I grow; I don't have lungs, but I need air; I don't have a mouth, but water kills me. What am I?

John was running from 40 thieves. John has got 3 gold boxes which weigh as 4kg, 2kg, and 1kg respectively. A witty man asked John to stay with him for seven days in exchange for 1kg gold per day. John needs to stay there for seven days and also do not want to give the witty man any advance. How can John pay for his seven days stay?

I look at you, you look at me, I raise my right, you raise your left. What am I?

John was driving a bus and got stuck when passing through an underpass. Then came Jacob with a needle and got the bus out of the underpass.

What did the boy do?