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

Take one out and scratch my head, I am now black but once was red. What am I?

Can you convert the number zero(0) into a positive number using just one mathematical operator ?

Can you calculate the probability of getting a sum of six when a dice is thrown twice?

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

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

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You need to remove two matchsticks to make the below equation true. Can you do it ?

If EELS + MARK + BEST + WARY = EASY

What does HELP + BARK + WARD + LEAD equal?

Can you find out who is the kidnapper in below Picture and why, Explain ?