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

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

In Greek mythology, the Sphinx sat outside of Thebes and asked this riddle of all travellers who passed by. If the traveller failed to solve the riddle, then the Sphinx killed him/her. And if the traveller answered the riddle correctly, then the Sphinx would destroy herself. The riddle:

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

Oedipus solved the riddle, and the Sphinx destroyed herself.

I am lying and I always lie. Tell me whether I am lying or telling the truth.

The world's largest Thanksgiving turkey was on display at a fair. Everyone was admiring it when suddenly a woman ran up and shot the turkey and left. Everyone knew her yet nobody made any attempts to stop or report her. Why?

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

I have 50 feet long of cloth, I need to create 50 handkerchiefs each size of 1 foot. I take one minute to cut a 1-foot handkerchief. So how long will it take to cut 50 handkerchiefs?

It is a nine-letter word.
The exact opposite of the phrase "friendly and outgoing"
It contains the word "over".
It starts will a vowel.

What is it?

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?