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

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

It has five wheels, though often think four, You cannot use it without that one more, You can put things in it, you can strap things on top, You can't find it in the market, but you can still go shop. What is it?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.

I am the beginning of the end, and the end of time and space. I am essential to creation, and I surround every place. What am I?

Today is John's birthday.
A year ago, John had five candles and he lit all the candles except the one at the last.
Now he is going to light all the candles.

How old is John Today?

(He is not five today.....)

Six glasses are in a row. The first three are filled with milk and the last three are empty. By moving only one glass, can you arrange them so that the full and the empty glasses alternate?

There are five vowels (a, e, i, o, u) in the English language.
Can you tell us a word that contains all these vowels?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?