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

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

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

Can you find the number?

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?

Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

A mules travels the same distance daily.
I noticed that two of his legs travels 10km and the remaining two travels 12km.
Obviously two mules legs cannot be a 2km ahead of the other 2.

The mules is perfectly normal. So how come this be true ?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

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