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

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

The first box has two white balls. The second box has two black balls. The third box has a white and a black ball.

Boxes are labeled but all labels are wrong!

You are allowed to open one box, pick one ball at random, see its colour and put it back into the box, without seeing the colour of the other ball.

How many such operations are necessary to correctly label the boxes?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

What is in seasons, seconds, centuries and minutes but not in decades, years or days?

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

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

They are three errirs in this question. Can you find them?

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?

How many Watermelons are there in the below picture?