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

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

In a town, there are four houses located at different distances from each other. Following are the distances:

The third house is 60 meters apart from the first house.
The fourth house is 40 meters apart from the second house.
The third house is 10 meters nearer to the fourth house than it is to the second house.

Can you find out the distance between the fourth and the first house?

Find out the missing number in the picture attached:

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

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?

Our product and our sum always give the same answer. Who are we?

How do you go from 98 to 720 using just one letter?

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.

John drives to his office at 20km/hr. After reaching the office, he realizes that today is a holiday. He went back at an average speed of 30km/hr. Discounting the time spent in the stoppage what was the average speed of his journey?