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

Known by all without exception, Forever here, for your protection, Sometimes strong, sometimes weak, Right after the night I come - hot and chic. And while millions of miles away, I always get to you, I find my way. No life around could do without me, Can you guess what I might be?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

It begins where the time ends.
Its second is an expression of surprise.
Its third is a question.
Its fourth is urinate.
It ends with a drink.

Which country it is?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

You have 1023 apples and 10 bags. You have to distribute these apples in these 10 bags in any way you choose. But when I ask for a certain number of apples you have to give them in terms of bags without transferring the apples from other bags. How do you distribute the apples?

Find the missing letter in the last circle logically in the given below picture.

I have branches, but no fruit, trunk or leaves. What am I?

Who is generally closer to the kids, mom or dad?

(it's a funny riddle)

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?