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

Sherlock breaks into a crime scene. The victim is the owner who is slumped dead on a chair and have a bullet hole in his head. A gun lies on the floor and a cassette recorder is found on the table. On pressing the play button, Sherlock hears the message 'I have committed sins in my life and now I offer my soul to the great Lord' and followed a gunshot Sherlock smiles and informed the police that's its a murder.

Why did he think so?

Solve the mathematical equation in the picture below.

There are four 3-link chains. All you have to do is join them into a big 12-link chain. For joining two closed links, one of the links must be cut and placed onto the other link for closing.

How many minimum links will you have to cut to make the big chain?

On her drawing table, Sayna lit 12 coloured candles. A few seconds later she blew two candles off.

How many candles Sayna have at the end?

Andrew sees a very rare bird named "Ruppell's vulture". Soon Andrew was dead. Can you explain the mystery, Mr. Sherlock?

How many words can a pen with half refill write?

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

Count the number of triangles in the given picture.

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?