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

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

You are confined in a room and given two metal rods. Out of these two rods, one is magnet and the other is the iron rod. They look starkly similar. You don't have any other metal object in the room.

How will you decide which one of those is magnet?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

What is next number in the pattern below:

131 517 192 123 ?

Why is it very easy to weigh a fish?

Solve the puzzle by telling what does below picture means.

Can you write down eight eights so that they add up to one thousand?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?