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

Four men were in a boat on the lake. The boat turns over, and all four men sink to the bottom of the lake, yet not a single man got wet! Why?

There is a circular car race track of 10km. There are two cars, Car A and Car B. And they are at the exact opposite end to each other. At Time T(0), Both cars move toward each other at a constant speed of 100 m/seconds. As we know both cars are at the same speed they will always be the exact opposite to each other.
Note, at the center, there is a bug which starts flying towards Car A at time T(0). When the bug reaches car B, it turns back and starts moving towards the car A. The speed of bug is 1m/second. After 5 hours all three stop moving.
What is the total distance covered by the bug?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

Take 9 from 6, 10 from 9, 50 from 40, and leave 6.

How Come ??

Two men play a dice game involving roll of two standard dice. Man X says that a 12 will be rolled first. Man Y says that two consecutive 7s will be rolled first. The men keep rolling until one of them wins.

What is the probability that X will win ?

Solve this riddle by finding the odd one out from the rest.

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

Christina is older than Kareena and Karishma. Katrina is older than Karishma and younger than Kareena. If Kareena has a brother named John, who is older than Christina, who's the youngest?

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?