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

A Shopkeeper collects 71 rupees in the form of 20 paisa and 25 paisa.
He collects a total of 324 coins.

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

You have $100 with you and you have to buy 100 balls with it. 100 is the exact figure and you can't go below or above the numbers and you have to use the entire $100. If there is no kind of tax applied how many of each of the following balls will you be able to buy:

Green Balls costing $6
Yellow Balls costing $3
Black Balls costing $0.10

Now, how many of each must you buy to fulfil the condition given?

Can you find out which number multiplied by itself will give the output as 12345678987654321?

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

'S' refers to the number of seconds in a day and 'H' refers to the number of hours in ten years. Which quantity out of these two is greater?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

If 21x = 79x, what is the value of x?