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

I am lying and I always lie. Tell me whether I am lying or telling the truth.

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

How can you write nineteen in a manner that if we take out one, it becomes twenty?

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

Count the number of lines in the image below ?

You order chicken wings at KFC in the boxes of 6, 9 and 20. What is the largest number of wings that you cannot obtain by buying in any combination of the boxes?

John bought 150 chocolates but he misplaced some of them. His Father asked him how many chocolates were misplaced.
He gave the following answer to him:
If you count in pairs, one remains
If you count in threes, two remain
If you count in fours, three remain
If you count in fives, four remain
If you count in sixes, five remain
If you count in sevens, no chocolate remains.

Can you analyze the statements and tell us how many chocolates were lost?

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

John replied, when asked how old he was. In 2 years he will be twice as old as he was five years ago.' How old is he ?