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

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?

Find the missing number in the sequence below:

What do you answer even though it never asks you questions?

It is a 5 letter word if you take away first letter it is something you get from sun, if you remove second letter you will get something to eat, if you remove third letter you get a word you use in pointing at and if you remove the fourth letter you get something to drink. What is it?

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

I have an eye but still cannot see.

Who am I?

What have one eye but still cannot see?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

Below the four parts have been reorganised. The four partitions are exactly the same in both arrangements. Why is there a hole?