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 once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

These types of puzzles are known as charades. What you have to do is to find two words that are referred to in the first stanza and the second stanza and put them together to form the third word in the third stanza.

Just for example, if my first refers to 'off' and my second refers to 'ice', then my whole will be the 'office'.

My first is present - future's past -
A time in which your lot is cast.

My second is my first of space
Defining people's present place.

My whole describes a lack of site -
A place without length, breadth, or height.

You have two buckets of 11 liters and 6 litres.
How can you measure exactly 8 litres?

A game is being played where eight players can last for thirty-five minutes. Six substitutes alternate with each player in this game. Thus, all players are on the pitch for the same amount of time including the substitutes.

For how long is each player on the pitch?

One day, I thought of ways that can be used for creating a palindrome. So I decided that I will turn into a larger number by adding the reversed digits to the original number and keep doing it till I finally obtained a palindrome.

I am not sure if this process will always result in a palindrome eventually but I was able to produce a four-digit palindrome. Can you guess my starting number?

When my father was 31 I was 8. Now he is twice as old as me. How old am I?

On a windy rainy night , I was driving in my car.
When i reach the bus stand , i see three people waiting for the bus.

1. An old lady who needs an immediate medical attention
2. My Best Friend
3. Girl whom i love from childhood

My car is a two seat, so can you tell me , what i have done in this situation ?

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?