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 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 ?

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)

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

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

I am an odd number. Take away a letter and I become even. What number am I?

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

If we add four times the age of John four years from now to five times his age five years from now we get ten times his current age.

How old will John be two years from now?

'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?