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

In my garden, I have many trees but only one of them is the mango tree. In these mango trees, there are some mangoes(as expected).

But after a strong wind, there are neither mangoes on the tree nor on the ground. Explain?

There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

Replace the question mark with the correct number.

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

Below rebus represent famous DiCaprio movie. Can you name it?

Remove two matchsticks to make the below equation correct.

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?

Eight of us go fourth, not back, to protect our king from an attack. What are we?