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?

A man is lying dead in a field where no one is around. His head is split open and his legs are disfigured. Near to him, there is an unopened package. No living organism can be found anywhere at the crime scene.

How did he die?

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

There was a strange boy who was born before his father. How can this be possible?

Can you find out the missing number?

? 4 5 3 5

9 5 7 10 3

It's a protector.
It sits on a bridge.
One individual can see directly through it, while others wonder what it hides.

What is it?

Using Only Five 5's and any mathematical operator make sum as 37

On a beautiful Sunday morning, You ordered a hot tea to your hotel room and suddenly you remember an important thing that needed to be done right now will take around 3 minutes to complete.
Like most people you like your tea to be hot while drinking so, when should you pour cream in the tea?
1. straight away
2. Just people, you drink the team
3. Its does not matter

What breaks yet never falls, and what falls yet never breaks?