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 was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

There are three houses in a straight row. One is red, one is blue, and one is white. The red house is left of the middle. The blue house is right of the middle. Where's the white house?

Four children having five rocks each were playing a game in which they had to throw the rock at a particular solid area in the water. Child 1- Succeeded in throwing three rocks at a solid area but one of the rocks sunk. Child 3 - His aim was so bad that all rocks got sunk. Child 4- He was awesome and none of the rocks got sunk. Child 2 - Was the winner but was struck by a rock in the head and died. Who killed Child 2?

Rebus Puzzle Definition: A rebus is an illusion device that uses pictures to represent words or parts of words.
What does This Rebus Puzzle Identify?

I got a bee but no honey.
got an eye but am still blind.
got a sea but no water.
got a tea but no coffee.
got a why but no answer.

What Am I?

1 + 9 + 8 = ?
considering, 28 + 8 + 92 = 10

There is a basket full of hats. Three are white and two are black. Three men, Tom, Tim, and Jim, each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves so Tom can see Tim and Jim’s hats, Tim can see Jim’s hat, and Jim can’t see anyone’s hat. Tom is asked what color his hat is and he says he doesn’t know. Tim is asked the same question, and he also doesn’t know. Finally, Jim is asked the question, and he does know. What colour is his hat?

In a jungle where there are no street lights or any other artificial source of lights, I notice a black snake crossing the road.
How did I get sight of the snake?

A mules travels the same distance daily.
I noticed that two of his legs travels 10km and the remaining two travels 12km.
Obviously two mules legs cannot be a 2km ahead of the other 2.

The mules is perfectly normal. So how come this be true ?