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 am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

Can you fill the blank with the correct number?

6 30 870 756030 _____

Can you find a number that lies one third of the distance between 1/3 and 2/3?

Rebus Puzzle Definition: A rebus is an illusion device that uses pictures to represent words or parts of words.
What does This Rebus Puzzle Identify?

Things are just as they seem, right? Well, check again.
Can you count the number of tigers in this picture ?

A man is sitting in a bar when a rich man sits next to him. He turns to the rich man and says, “Did you know I know almost every song that has ever existed?”

The rich man laughs. The man then says, “I bet you all the money you have in your wallet that I can sing a genuine song with a lady’s name of your choice in it. The rich man laughs again and says, “OK, how about my daughter’s name, Jamie Armstrong-Miller?” Minutes later, the man collects his cash and the rich man goes home cashless. What song did the man sing?

The richest man in the city Mr Rechard is kidnapped. James Bond is appointed to the case. At the crime scene, a note is found written by Mr Richard. The note read:

"First of January, Fourth of October, Fifth of March, Third of June."

James Bond knew that somehow, the killer's name was hidden in the note. The following were the suspects:

Jack Richard, the son and the heir of property.
John Jacobson, the employee of Richard.
June Richard, the wife of Richard.

James Bond took only a few moments to deduce the killer's name. Can you tell who was the killer?

A frog is at the bottom of a 30-meter well. Each day he summons enough energy for one 3-meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?