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 can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

Can you spot the man between the coffee bean in the picture below ?

A man is found dead with a knife in his back When the investigation is done. A chair lays beside him and the forensic team finds moisture around the body.

If he committed suicide, how did he do it?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

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

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

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.

A man wants to cross the pit of fire which is 25 feet in length and he has 2 planks(fire resistant) 19 feet in length. How can he cross the pit of fire alive?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?