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

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

Replace the question mark with the number below given a simple math problem.

I always drive my customer away.

Who am I?

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

There’s a girl who has a large family. She has an equal amount of brothers and sisters, but each brother only has half as many brothers and sisters. What’s the correct amount of brothers and sisters?

What have one eye but still cannot see?

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

An artist while painting a scenic beauty, decides to paint three layers of blue colour on the sky.

Which layer will go on the first?