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 has a barrel filled with oil that weighs 100 pounds, and then he puts something into it. Now the barrel weighs less than 100 pounds. What did he put in the barrel?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

Always in you, Sometimes on you;

If I surround you, I can kill you.

What am I?

Can you find out the remainder when 3^300 is divided by 5?

Take one out and scratch my head, I am now black but once was red. What am I?

Here is a conversation between a couple who both are software professionals.

Husband: Hey! What is your date of birth?
Wife Replied Angrily: It is 591062400
Husband after doing some calculations replied, "Got It".

What is the DOB of the wife?

What work can one never finish?

To tease, King Akbar told his most clever advisor Birbal to give his daughter one thing that she can eat when hungry, drink if she feels thirsty and can burn if she feels cold. King Akbar was shocked when Birbal gave Akbar's daughter one such thing that satisfies all of the above.

What did Birbal give to Akbar's daughter?

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 ?