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

10+10 and 11+11 can give you the same answer.

Explain how?

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?

There are five vowels (a, e, i, o, u) in the English language.
Can you tell us a word that contains all these vowels?

A new clothing store has a unique method of pricing items. A vest costs $20, a tie costs $15, a blouse costs $30, and underwear costs $45. How much would pants cost?

I am taken from a mine and shut up in a wooden case, from which I am never released, and yet I am used by almost every person. What am I?

Doctor Alex and a bus driver John are both in love with the same woman named Olivia. The bus driver need to go for a long trip of 10 days, Before he left he gave Olivia 10 apples.

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

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

What is the word or phrase?