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

There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

Open a Laptop which is password protected. Hint for the password is given as below:

1 mobile 3 books 2 Boards 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches

A Child was born in Lahore, Pakistan.

Still child is not a Pakistani citizen.why ?

Write the next letter in this sequence.
O, T, T, F, F, S, S, E, __
**Hint: It is a Number Series Puzzle

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

Why 1729 is a magic number? Answer Logically.

They do not possess flesh or feathers or scales or bone
But still, they are blessed with fingers and thumbs of their own.

Okay before we begin with the puzzle, do keep in mind that you have to answer it quickly.

You are participating in a car race. Seeking the perfect moment, you overtake the second person in the race. What positions are you in now?

Our product and our sum always give the same answer. Who are we?