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

I am dry when I go inside, but wet when I am pulled outside.
The longer I am inside, the stronger I get
When I am completely out, I am wet and I literally sag
Who am I?

How many times can you subtract the number two from the number fifty?

You are an expert on paranormal activity and have been hired to locate a spirit haunting an old resort hotel. Strong signs indicate that the spirit lies behind one of four doors. The inscriptions on each door read as follows:

Door A: It's behind B or C
Door B: Its behind A or D
Door C: It's in here
Door D: It's not in here

Your psychic powers have told you three of the inscriptions are false, and one is true. Behind which door will you find the spirit?

Can you guess the name of the month by looking the below rebus ?

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

In the given figure, you can see that four match sticks are used to form a square. Can you form five squares by using six matches?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

The doctor advised his patient to take a tablet after every fifteen minutes. He gave him five tablets in total.

How much time will he take to have all the five tablets?

When 99 is considered higher than 100?