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 container contains 100 eggs. They can be either fresh or rotten. What is sure is the fact that there is at least one fresh egg in that container.

If you are asked to pick two eggs randomly from the container, at least one of them will be rotten.

Can you calculate how many eggs in that container are fresh?

If we add four times the age of John four years from now to five times his age five years from now we get ten times his current age.

How old will John be two years from now?

Which digit occurred maximum times between the number 1 and 1000?

John and his wife were living in a rural place. On a particular day, John's wife fell ill and he called the local doctor. When the doctor picked up, he said, "Doctor, my wife is ill. She might have appendicitis."

"This can't be possible! I took out her appendix two years ago myself," the doctor explained.

When diagnosed, John's wife was found to have appendicitis. How can this be possible?

Divide 110 into two parts so that one will be 150 per cent of the other. What are the 2 numbers?

What can you catch but never throw?

You need to arrange three 7 and mathematical symbols to form number 1?

There is a brick of gold and a brick of iron in a boat (both 10-inch blocks), if they are both dropped into the water which will make the water level higher?

There were three women in all the swimming costumes!
One was happy and the other two were sad!
The happy one was crying and the sad ones were smiling.
Why was this?