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

John is pretty weird. He likes toffees but hates chocolates. He loves books but never reads. He likes to build his troops in an online game but does not proceed with the war. He likes to go swimming but is afraid of water.

Seeking this behaviour, can you tell whether he likes balloons and parties?

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?

There are three boxes. One is labeled "APPLES" another is labeled "ORANGES". The last one is labeled "APPLES AND ORANGES". You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.

How can you label the boxes correctly?

Forwards I am heavy, backward I am not. What am I?

Two-person want to cross a river. Only one boat is present on the riverside that can carry only one person at a time.

However, they still manage to cross the river. How is it possible?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

What's the next in the series?

H, Be, F, S, Mn, Kr, In, Gd, Tl, ?

I make a loud sound when I’m changing. When I do change, I get bigger but weigh less. What am I?