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

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

If "P" means "-", "Q" means "/", "R" means "+", and "S" means "*" then find the value of the following:

21 Q 7 R 9 S 10 P 13

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?

What is the end of everything?

If two's company, and three's a crowd, then whats four and five ?

John is looking at Jenifer, but Jenifer is looking at Jacob. John is married, but Jacob is not.

Is a married person looking at an unmarried person ?

I have a big mouth and I am also quite loud! I am NOT a gossip but I do get involved with everyone's dirty business.

Can you count the number of seconds in a year?

Clue: You need to bother about calculation.

John buys rice at Rs.60/kg from Britain and then sells them at Rs.5/kg in India. As a result of this, he becomes a millionaire. How come?