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

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

Can you name an animal whose killing cannot be performed without spilling your own blood?

I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?

Decode below three cipher riddles:

26 L of the A
7 D of the W
1000 Y in a M

If eleven plus two equals one, what does nine plus five equal?

I am the first thing you need while camping.
I am always with the person named Marcos Valencia and Carrick.
But Pogba Zlatan and Rooney think I am wasteful and do not need me.
I am the second to the last thing to add when you are making a patch.

What am I?

There are seven sisters in a house in a village where there is no electricity or any gadget.

Sister-1: Reading Novel
Sister-2: Cooking
Sister-3: Playing Chess
Sister-4: Playing Sudoku
Sister-5: Washing clothes
Sister-6: Gardening

what is Sister-7 doing ?

Imagine you are in a room with no windows or doors. How will you get out?

What does below science rebus mean?

Ag Ag Ag
Ag SPOON Ag
Ag Ag Ag