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

What has hands, but can’t clap?

I am sure no one can have two things for dinner. what are they?

Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

Whats the next number in the below number sequence pattern.

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

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?”

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

Can you find a rabbit in the given picture?