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

The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

Three brothers Jacob, John, and James live in Mexico City. The product of the ages of these brothers is 175. Jacob and John are twins. How old is James?

What building has the most stories?

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

What runs around the whole yard without moving?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?