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

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?

He digs out tiny caves and stores gold and silver in them. He also built bridges of silver and made crowns of gold. They are the smallest you could imagine. Sooner or later everybody needs his help, yet many people are afraid to let him help them. Who is he?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

Can you count the number of children in the picture below

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

Outside a tattoo artist's shop, there was a signboard which read 'I make tattoos on only them who do not tattoo themselves'.

Reading it what do you think, does the tattoo artist tattoo himself?

Women do it once a year after they turn 19 but men get to do it only once in a lifetime. What is it?

Imagine you are in a room with no windows or doors. How will you get out?

Kareena is older than Katrina and younger than Karishma. Isabelle is younger than Bipasha and Karishma. Bipasha is older than Karishma. If Kareena and Isabelle are the same age, who's the youngest?