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 has a bottom at the top?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

You throw me out when you want to use me and you take me in when you don't want to use me.

Who Am I?

Five thieves looted a bank and they ran away in a car. The bank staff informed the police and they began the search of their car in their jeep. They found them on a road and chased them eventually catching them. The light that is used to fill the number plate was broken on the thieves' car. Also, the headlights of the jeep police were not working. How were the police able to catch the thieves then?

Once while in his court, King Akbar asked Birbal to write something on a wall that makes one sad when read in good times and makes one happy when read in sad times.

He took only a few moment and wrote something that fit the requirements. What did he write?

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

Move four matchsticks to the below square to form three squares?

A new Engineering building containing 100 offices had just been completed. John was hired to paint the numbers 1 to 100 on the doors. How many times will John have to paint the number nine (9)?

What is the centre of gravity?