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

On one occasion, A Boy collects 71 rupees in form of 20 paise and 25 paise. He collects a total of 324 coins.

Can you tell me how many 20-paisa and 25-paisa he got?

Three friends decide to distribute the soda cans they had among them. When all of them had drunk four cans each, the total number of cans that remained was equal to the cans each one of them had after they had divided the cans.

Can you calculate the total number of cans before distribution?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

A number can be multiplied by multiple of nine
i.e 9 18 27 36 45 ...

and the resulting number consist of only one digit.

Can you identify the number ?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

Find three whole, positive numbers that have the same answer when multiplied together as when added together.

You need to arrange three 7 and mathematical symbols to form number 1?