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

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

Once upon a time, there was a castle on a square island. The entire island was surrounded by a 14m wide trench. The Romans had wanted to invade the castle and had brought a few wooden planks along with them to facilitate themselves in crossing the moat. The planks were however found to be only 13m long.

The Romans still managed to cross the trench. How did they do it?

Which flower has two lips?

In the given figure, you can see that four match sticks are used to form a square. Can you form five squares by using six matches?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

Which digit occurred maximum times between the number 1 and 1000?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

There is a box. The area of its top is 240 square units, the area of the front is 300 square units and the area of the end is 180 square units.

Can you calculate the dimensions of this box with the given data?