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

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?

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 ?

A generous owner of a company decided to give a bonus of $45 to every man and $60 to every woman on his birthday. But only one-ninth of the men and one-twelfth of the women were present to take the bonus.

Can you calculate the amount of money the owner spent if there were 3552 employees?

Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation. Conditions: Each must be used exactly once and no other numbers or symbols can be used.

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

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?

'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?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?