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

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

Shyla was sleeping in her apartment when suddenly a robber broke into her house. He asked her to stay quiet and started looting the cash and jewelry. Suddenly the landline phone started ringing. The robber pointed a gun at Shyla and asked her to pick up and talk without giving away the situation.

She picked up the phone and it happened to be her husband. She spoke, Is it an emergency darling? Do give me a call when your flight lands, I will prepare your favorite food that will help you relieve the stress. Then she hanged up.

10 minutes after, the police arrive at the scene and catch the robber. How did the police know about the robbery?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

I guess 76.8% of readers will like this riddle.

What's the least number of people should read this post?

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 ?

You and your two friends are working in a multinational company. How can you three find out the average salary of you all without disclosing your own salary to the other two?

You are trapped in a room with two doors. One leads to certain death and the other leads to freedom. You don't know which is which.
There are two robots guarding the doors. They will let you choose one door but upon doing so you must go through it.
You can, however, ask one robot one question. The problem is one robot always tells the truth, the other always lies and you don't know which is which.
What is the question you ask?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I