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

John was piloting a plane behind a car but was never able to overtake it. Why?

Astrology starts with the alphabet A, Biology starts with B, Psychology with P and Limnology with L.

Can you find an "ology" that begins with a P?

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

A man is sitting in a bar when a rich man sits next to him. He turns to the rich man and says, “Did you know I know almost every song that has ever existed?”

The rich man laughs. The man then says, “I bet you all the money you have in your wallet that I can sing a genuine song with a lady’s name of your choice in it. The rich man laughs again and says, “OK, how about my daughter’s name, Jamie Armstrong-Miller?” Minutes later, the man collects his cash and the rich man goes home cashless. What song did the man sing?

Railroad Crossing, look out for the cars. Can you spell that, without any R's ?

2, 3, 5, 9, 17, _ What is the next number in the sequence?

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

Solve The below Equation:

ALFA + BETA + GAMA = DELTA