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

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

John killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

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?

Move four matchsticks to the below square to form three squares?

Take 9 from 6, 10 from 9, 50 from 40, and leave 6.

How Come ??

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?