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

A woman is sitting in her hotel room and hears a knock at the door. She opens the door to see a man whom she’s never met before. He says, “I’m sorry, I have made a mistake, I thought this was my room.” He then goes down the corridor and into the elevator. The woman goes back into her room and calls security. What made the woman so suspicious of the man?

How many triangles are there in the picture below?

Can it be possible to build a house that has all its four walls facing towards the South?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

Many have heard it, but nobody has ever seen it, and it will not speak back until spoken to. What is it?

Two fathers and two sons decided to go to a shop and buy some sweets upon reaching. Each of them bought 1 kg of sweet. All of them returned home after some time and found out that they had 3kg of sweets with them.

They did not eat the sweets in the way, nor threw or lose anything. Then, how can this be possible?

The Federal bank of London is abducted by the robbers. The head of the robbers asked the cashier to empty their money vault to them and when suddenly cashier got a call from her father. To avoid any suspicion, the robber asked the cashier to pick the call and reply her father in the shortest manner possible.

The cashier told her father "Is there an emergency father, Call me when you are free and I will help you in your furnishing" and then the cashier hung up the phone.

After 10 minutes, police arrived at the crime scene.

How did the police know about the robbery?

What is next number in the pattern below:

131 517 192 123 ?

I have 50 feet long of cloth, I need to create 50 handkerchiefs each size of 1 foot. I take one minute to cut a 1-foot handkerchief. So how long will it take to cut 50 handkerchiefs?