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

Suppose that you are trapped on the surface of a frozen lake. The surface is so smooth and ideal that there is no friction at all. You cant make any grip on the ice and no wind is blowing to help you out. You have just a mobile phone with you which has got no reception disabling you to call for help.

How will you plan your escape before you freeze to death on the frozen lake?

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

Can you arrange the six given marbles in a manner that each one of them is touching all four marbles of different colours?

What common phrase is represented by the below lines

Easy going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Medium going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Tough going:
Weak, 'I can't do it, I'm staying!'
Tough, 'Let's get going.'

There is a straight highway. Four different villages lie on that highway. The distance between them is different. The third village is 60km away from the first village; the fourth is 40 km away from the second; the third is 10 km near to the fourth that it is to the second.

Can you calculate the distance between the fourth and the first village ?

John went to meet his friend Jacob, but when he was about to reach the main gate, John notices that Jacob had a mighty dog who was fastened to the tree. The chain is long enough that it allows the dog to reach the main gate.

How can the John reach the main gate?

Find the smallest sentence with all the English alphabet.

Before Mount Everest was discovered, what was the highest mountain in the world?

You are camping with your friends. You have a flashlight for any emergency and have brought 8 batteries along with you. Your brother calls to tell you that four of those batteries are already dead.

Your flashlight requires two working batteries to run. What is the least number of pairs you will need to test to guarantee that you can get the flashlight on?