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

Out of three Friends John, Jacob and Jonny one of them is a king, one is a bureaucrat, and one is a Spy.

The king always tells the truth, the bureaucrat always lies, and the Spy can either lie or tell the truth.

John says: Jonny is a bureaucrat
Jacob says: John is a king
Jonny says: I am a Spy

Tell me, Who is the king, who is the bureaucrat, and who is the Spy?

It's a test that will check your IQ.

Suppose you have one 11 minute hourglass and one 13 minute hourglass.

Can you measure exactly fifteen minutes using them ?

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

When a clock is observed, the hour hand is at a minute mark and the minutes hand is six minutes ahead of it.

When the clock is observed again after some time, the hour hand is precisely on a different minute mark and the minute hand is seven minutes ahead of it.

Can you calculate how much time has elapsed between the two observations?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

My first is in chocolate but not in ham. My second is in cake and also in jam. My third at tea time is easily found. Altogether, this is a friend who is often around. What is it?

Do you know of a place where the wind blows south and then suddenly shifts direction towards the north?