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

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

He loves to dance, twist and prance, he shakes his tail, and as a way he sails, wingless he flies into the sky. What is he?

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

In this image, you can see three almost identical Doraemon images. Can you spot the odd one out from them?

Jessica is telling her friends this story and asks them to guess if it’s the truth or a lie: “There was a man sitting in a house at night that had no lights on at all. There was no lamp, no candle, and no other source of light. Yet, he sat in the house and read his book happily.” Her friends say she’s lying, but Jessica corrects them and says she’s telling the truth. Jessica’s story is true—but how?

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?

Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
All puppets are of different size. She arrange all puppets to face towards the guest and tell the guess the following clues :

* Jane has three puppets bigger on its left side
* Bird has two puppets smaller on its left side
* Barbie has one puppet bigger on its right side
* Angel has two puppets smaller on its right side
* Colleen has one puppet bigger on its left side
* Nora has one puppet smaller on its left side
* Lass has four puppets bigger on its right side
* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

Assuming you are the guest , can you tell the katty how the puppets are arranged ?

A man and a dog were going down the street. The man rode, yet walked. What was the dog’s name?