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?

What does below chemistry rebus means?

What is the last thing you take off before bed?

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?

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

There are two dice with empty faces in front of you and a marker. You can mark any number on each of the faces of the two dice, but you have to display all 31 days of the month using the two of them.

Which numbers will you mark on which dice so that you can easily depict all the dates of the month?

Can you solve this tricky maths equation problem by replacing it? mark with the correct symbol?

19834 -----: 187
15921 -----: 153
17561 -----: 139
13734 -----: ???

People put me on the table and cut me but do not eat me. What am I?