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 rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

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

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

Can you solve this tricky maths equation problem by replacing it? mark with the correct symbol?

19834 -----: 187
15921 -----: 153
17561 -----: 139
13734 -----: ???

In case you were starting to feel confident, this one was meant for third graders in Vietnam. The answer is 66, but we don't blame you for scratching your head about how they got there.

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

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

Can you find the number?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209