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

For an extra income, John decided to work at a Hotel for one hour daily. The manager offers him that they will pay him $11 after every 11 days.
However, John offered a different proposition to the manager. The offers stand as:
He will be paid just a penny on his first day.
Two pence will be paid on the second day,
Four pence will be paid on the third day.
And so on till the 11th day.

Should the Hotel manager accept his offer?

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?

There are 20 people in an empty, square room. Each person has full sight of the entire room and everyone in it without turning his head or body, or moving in any way (other than the eyes). Where can you place an apple so that all but one person can see it?

In the following series, a set of numbers is progressing with a particular pattern. Can you deduce that pattern and find the missing set?

(2 + 6), (21 + 6), (58 + 6), (119 + 6), ___

What has a bottom at the top?

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

Can you find out the missing number?

? 4 5 3 5

9 5 7 10 3

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 is the end of everything?