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

Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

I inserted a coin in a bottle and closed its mouth with the help of a cork. Now, I was able to take the coin out from the bottle without taking out the cork or breaking the bottle. Can you tell me how I did it?

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

What are the next two letters in the following series and why?
W A T N T L I T F S _ _

*Hint: Check Puzzle Title

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.

Solve the equation in the image by looking at the pattern closely.

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

Whats the next number in the below number sequence pattern.

Imagine you are in a room with no windows or doors. How will you get out?