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

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

What number divided by 4 is the same as that number minus 4?

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours?

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

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

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?

By using all numbers, i.e. 123456789 and subtraction/addition, operators number 100 can be formed in many ways.
Example: 98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100

But if we add a condition use of the number 32 is a must. Then there are limited solutions.
One of such solution is: 9 - 8 + 76 + 54 - 32 + 1 = 100

Can you tell me any other solution?

Can you make the number 24 by utilizing the numbers 1, 3, 4 and 6? You must use one number only one time and you can use mathematical operation symbols anytime anywhere.

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.