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

When it's bad luck to meet a black cat?

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

In the below-given picture of a pretty girl, there is something wrong. Can you find out what it is?

He digs out tiny caves and stores gold and silver in them. He also built bridges of silver and made crowns of gold. They are the smallest you could imagine. Sooner or later everybody needs his help, yet many people are afraid to let him help them. Who is he?

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Can you calculate the distance between the fourth and the first village ?