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 plane crashed between the border of Mexico and America. Where do you bury the survivors?

A red house is made out of red bricks. A yellow house is made out of yellow bricks. And, a blue house is made out of blue bricks. So, what is a greenhouse made of?

If you paint a brown house white it will become a white house. If the stoplight changes from red to green, then the light is green. So, if you throw a white shirt into the Red Sea, what will it become?

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

If a zookeeper had 100 pairs of animals in her zoo, and two pairs of babies are born for each one of the original animals, then (sadly) 23 animals don’t survive, how many animals do you have left in total?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
Example: 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100

But if we add a condition use of the number 32 is a must. Then there are limited solutions.
One of such solution is: 9 - 8 + 76 + 54 - 32 + 1 = 100

Can you tell me any other solution?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.