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 high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

Can you write down eight eights so that they add up to one thousand?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Can you find the missing number in the third row?
35 20 14
27 12 18
5 2 ?

In a school, there are four subjects. Seventy percent of students study English, seventy five percent of students study Science, eighty five percent of students study Mathematics and eighty percent of students study Spanish.

Can you calculate the percentage of students that study all four subjects?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

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.

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

Can you find the number?

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