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

Tell me the Hindi name of a Vegetable which if we remove 1st word will become a precious Stone and by removing the last word it will become a sweet eatable.

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

In the four images below, can you find the odd one out?

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

The captain of a ship is telling you an interesting story and then poses a question. He says, “I have travelled the oceans far and wide. One time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly. Can you tell me how that was possible?”

How can you leave a room with two legs and return with six legs?