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

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

A police officer was passing by when he saw a guy hiding. He walked up to him and genially asked, "What is your name?"

"Shut up!" the boy responded.

"Where are your manners?" asked the outraged police officer.

"Up that tree," said the boy discourteously, directing to a neighbouring tree.

You're looking for trouble, aren't you?" said the police officer.

"No, trouble is looking for me!" the boy answered solemnly.

Why is the boy behaving like this?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

Can you find a rabbit in the given picture?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

It is a nine-letter word.
The exact opposite of the phrase "friendly and outgoing"
It contains the word "over".
It starts will a vowel.

What is it?