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

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

A B C D E F G H

These are the letters given to you. Now you have to find out the letter that comes two to the right of the letter which is immediately to the left of the letter that comes three to the right of the letter that comes midway between the letter two to the left of the letter C and the letter immediately to the right of the letter F.

A Shopkeeper collects 71 rupees in the form of 20 paisa and 25 paisa.
He collects a total of 324 coins.

Can you tell me how many number of 20-paisa and 25-paisa he got?

Can you make a six-letter word using the letters N, A and B ?

After a heavy Thanksgiving meal, the night watchman went to work. In the morning, he told his boss he had dreamed that a saboteur planted a bomb in the factory and that he felt it was a warning. The boss promptly fired him. Worker confused, Why boss fire him?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?