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

f you were running a race, and you passed the person in 2nd place, what place would you be in now?

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

A bomb exploded in a room full of married couples and no one died. How?

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?

Can you spot what's wrong with the following sentence?

PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.

I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.

What am I?

"That Restaurant always remains crowded. This is the reason why nobody goes there".

Can you find a flaw in this statement?

You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game.

Would you want to play first or second?

PS: The sum should be exactly 15.

When I go in I might cause pain. I cause you to spit and ask you not to swallow. I can fill your hole. What am I?