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 number that lies one third of the distance between 1/3 and 2/3?

I am a number I am not an odd number I am higher than 90 I am not higher than 100 If you subtract me from 100, you get nothing. What number am I?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

In a stable, there are men and horses. In all, there are 22 heads and 72 feet. How many men and how many horses are in the stable

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

At a Society election for president, precisely 963 votes were cast.
There is a total of 4 candidates that participate in the election.

The winning candidate exceeds the opponents by 53, 79 and 105 votes.

How many votes do each candidate gets?

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

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 ()

There is a number which when you multiply by 3 and subtract 2 from the result, then the resulting number is the reverse of the actual number.

What is the smallest number that stands true on the statement?